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0001 @comment{x-kbibtex-encoding=utf-8} 0002 0003 @article{Couso-Moral-2011, 0004 abstract = {The theory of sets of desirable gambles is a very general model which covers most of the existing theories for imprecise probability as special cases; it has a clear and simple axiomatic justification; and mathematical definitions are natural and intuitive. However, much work remains to be done until the theory of desirable gambles can be considered as generally applicable to reasoning tasks as other approaches to imprecise probability are. This paper gives an overview of some of the fundamental concepts for reasoning with uncertainty expressed in terms of desirable gambles in the finite case, provides a characterization of regular extension, and studies the nature of maximally coherent sets of desirable gambles, which correspond to finite sequences of probability distributions, each one of them defined on the set where the previous one assigns probability zero.}, 0005 author = {Inés Couso and Serafín Moral}, 0006 doi = {10.1016/j.ijar.2011.04.004}, 0007 journal = {International Journal of Approximate Reasoning}, 0008 localfile = {article/Couso-Moral-2011.pdf}, 0009 number = {7}, 0010 pages = {1034–1055}, 0011 title = {Sets of desirable gambles: conditioning, representation, and precise probabilities}, 0012 volume = {52}, 0013 year = {2011} 0014 } 0015 0016 @incollection{Quaeghebeur-2012-itip, 0017 author = {Erik Quaeghebeur}, 0018 booktitle = {Introduction to Imprecise Probabilities}, 0019 editor = {Frank P. A. Coolen and Thomas Augustin and Gert {De Cooman} and Matthias C. M. Troffaes}, 0020 publisher = {Wiley}, 0021 title = {Desirability}, 0022 year = {at the editor} 0023 } 0024 0025 @incollection{Morishima-1964-Perron-Frobenius, 0026 author = {Michio Morishima}, 0027 booktitle = {Equilibrium, stability, and growth}, 0028 chapter = {Appendix}, 0029 edition = {1967}, 0030 localfile = {inbook/Morishima-1964-Perron-Frobenius.pdf}, 0031 note = {ook op papier}, 0032 pages = {195–215}, 0033 publisher = {Oxford University Press}, 0034 title = {Generalizations of the Perron–Frobenius Theorem for nonnegative square matrices}, 0035 year = {1964} 0036 } 0037 0038 @article{DeCooman-Quaeghebeur-2010-Kyburg, 0039 abstract = {Sets of desirable gambles constitute a quite general type of 0040 uncertainty model with an interesting geometrical interpretation. We give a 0041 general discussion of such models and their rationality criteria. We study 0042 exchangeability assessments for them, and prove counterparts of de Finetti's 0043 finite and infinite representation theorems. We show that the finite 0044 representation in terms of count vectors has a very nice geometrical 0045 interpretation, and that the representation in terms of frequency vectors is 0046 tied up with multivariate Bernstein (basis) polynomials. We also lay bare the 0047 relationships between the representations of updated exchangeable models, and 0048 discuss conservative inference (natural extension) under exchangeability and the 0049 extension of exchangeable sequences.}, 0050 author = {Gert {De Cooman} and Erik Quaeghebeur}, 0051 doi = {10.1016/j.ijar.2010.12.002}, 0052 journal = {International Journal of Approximate Reasoning}, 0053 title = {Exchangeability and sets of desirable gambles}, 0054 year = {in press} 0055 } 0056 0057 @incollection{Dayhoff-Schwartz-Orcutt-1978, 0058 author = {M. O. Dayhoff and R. M. Schwartz and B. C. Orcutt}, 0059 booktitle = {Atlas of Protein Sequence and Structure}, 0060 chapter = {22}, 0061 editor = {M. O. Dayhoff}, 0062 localfile = {inbook/Dayhoff-Schwartz-Orcutt-1978.pdf}, 0063 pages = {345–352}, 0064 publisher = {National Biomedical Research Foundation}, 0065 title = {A Model of Evolutionary Change in Proteins}, 0066 year = {1978} 0067 } 0068 0069 @misc{Quaeghebeur-2010-SSS, 0070 author = {Erik Quaeghebeur}, 0071 howpublished = {Lecture at the 4th SIPTA Summer School, Durham, UK}, 0072 title = {Inference \& Desirability}, 0073 url = {http://users.ugent.be/~equaeghe/#EQ-2010-SSS}, 0074 year = {2010} 0075 } 0076 0077 @article{Buckley-1995, 0078 abstract = {We propose a new solution concept for fuzzy programming 0079 problems. It is based on our new method of solving fuzzy equations [10]. For 0080 simplicity we discuss in detail only fuzzy linear programming in this paper. We 0081 define, and obtain the basic properties of the joint solution (a fuzzy vector in 0082 R^n) and the optimal value of the objective function (a fuzzy number). Three 0083 examples are presented illustrating these concepts.}, 0084 author = {J. J. Buckley}, 0085 doi = {10.1016/0165-0114(94)00353-9}, 0086 issn = {0165-0114}, 0087 journal = {Fuzzy Sets and Systems}, 0088 keywords = {mathematical programming}, 0089 localfile = {article/Buckley-1995.pdf}, 0090 number = {2}, 0091 pages = {215–220}, 0092 title = {Joint solution to fuzzy programming problems}, 0093 volume = {72}, 0094 year = {1995} 0095 } 0096 0097 @article{Peterson-1972-Radon, 0098 author = {B. B. Peterson}, 0099 journal = {The American Mathematical Monthly}, 0100 localfile = {article/Peterson-1972-Radon.pdf}, 0101 number = {9}, 0102 pages = {949–963}, 0103 title = {The geometry of Radon's theorem}, 0104 url = {http://www.jstor.org/stable/2318065}, 0105 volume = {79}, 0106 year = {1972} 0107 } 0108 0109 @book{BenHaim-2006-info-gap, 0110 author = {Yakov Ben-Haim}, 0111 edition = {2}, 0112 publisher = {Academic Press}, 0113 title = {Info-Gap Decision Theory: Decisions Under Severe Uncertainty}, 0114 year = {2006} 0115 } 0116 0117 @inproceedings{Mevel-Finesso-2000, 0118 annote = {ook op papier}, 0119 author = {Laurent Mevel and Lorenzo Finesso}, 0120 booktitle = {Fourteenth International Symposium on Mathematical Theory of Networks and systems: MTNS 2000}, 0121 title = {Bayesian estimation of Hidden Markov Models}, 0122 year = {2000} 0123 } 0124 0125 @article{Fagiuoli-Zaffalon-1998-2U, 0126 abstract = {This paper addresses the problem of computing posterior 0127 probabilities in a discrete Bayesian network where the conditional distributions 0128 of the model belong to convex sets. The computation on a general Bayesian 0129 network with convex sets of conditional distributions is formalized as a global 0130 optimization problem. It is shown that such a problem can be reduced to a 0131 combinatorial problem, suitable to exact algorithmic solutions. An exact 0132 propagation algorithm for the updating of a polytree with binary variables is 0133 derived. The overall complexity is linear to the size of the network, when the 0134 maximum number of parents is fixed.}, 0135 author = {Enrico Fagiuoli and Marco Zaffalon}, 0136 doi = {10.1016/S0004-3702(98)00089-7}, 0137 issn = {0004-3702}, 0138 journal = {Artificial Intelligence}, 0139 keywords = {Bayesian networks; convex sets; credal sets; intervals; uncertain reasoning}, 0140 localfile = {article/Fagiuoli-Zaffalon-1998-2U.pdf}, 0141 month = nov, 0142 number = {1}, 0143 pages = {77–107}, 0144 publisher = {Elsevier}, 0145 title = {2U: an exact interval propagation algorithm for polytrees with binary variables}, 0146 volume = {106}, 0147 year = {1998} 0148 } 0149 0150 @article{Edwards-1983-Pascal, 0151 author = {A. W. F. Edwards}, 0152 journal = {International Statistical Review}, 0153 localfile = {article/Edwards-1983-Pascal.pdf}, 0154 pages = {73–79}, 0155 title = {Pascal's Problem: The ‘Gambler's Ruin’}, 0156 url = {http://www.jstor.org/stable/1402732}, 0157 volume = {51}, 0158 year = {1983} 0159 } 0160 0161 @book{Friedman-1989feron, 0162 annote = {geannoteerde uittreksels}, 0163 author = {James W. Friedman}, 0164 keywords = {game theory; mathematical economics}, 0165 publisher = {Oxford University Press}, 0166 title = {Game Theory with Applications to Economics}, 0167 year = {1989} 0168 } 0169 0170 @article{Hipp-1974, 0171 author = {Christian Hipp}, 0172 doi = {10.1214/aos}, 0173 journal = {The Annals of Statistics}, 0174 localfile = {article/Hipp-1974.pdf}, 0175 month = nov, 0176 number = {6}, 0177 pages = {1283–1292}, 0178 title = {Sufficient statistics and exponential families}, 0179 url = {http://www.jstor.org/stable/2958344}, 0180 volume = {2}, 0181 year = {1974} 0182 } 0183 0184 @article{Dempster-1968, 0185 abstract = {Procedures of statistical inference are described which 0186 generalize Bayesian inference in specific ways. Probability is used in such a 0187 way that in general only bounds may be placed on the probabilities of given 0188 events, and probability systems of this kind are suggested both for sample 0189 information and for prior information. These systems are then combined using a 0190 specified rule. Illustrations are given for inferences about trinomial 0191 probabilities, and for inferences about a monotone sequence of binomial p\_i. 0192 Finally, some comments are made on the general class of models which produce 0193 upper and lower probabilities, and on the specific models which underlie the 0194 suggested inference procedures.}, 0195 annote = {with discussion}, 0196 author = {Arthur P. Dempster}, 0197 journal = {Journal of the Royal Statistical Society. Series B (Methodological)}, 0198 localfile = {article/Dempster-1968.pdf}, 0199 number = {2}, 0200 pages = {205–247}, 0201 title = {A generalization of Bayesian inference}, 0202 url = {http://www.jstor.org/stable/2984504}, 0203 volume = {30}, 0204 year = {1968} 0205 } 0206 0207 @article{Koopman-1940-ams, 0208 author = {B. O. Koopman}, 0209 journal = {Bulletin of the American Mathematical Society}, 0210 localfile = {article/Koopman-1940-ams.pdf}, 0211 number = {10}, 0212 pages = {763–774}, 0213 title = {The bases of probability}, 0214 url = {http://www.ams.org/bull/1940-46-10/S0002-9904-1940-07294-5/S0002-9904-1940-0729 0215 4-5.pdf; http://projecteuclid.org/euclid.bams/1183503229}, 0216 volume = {46}, 0217 year = {1940} 0218 } 0219 0220 @article{Cozman-2005-graphical, 0221 abstract = {This paper presents an overview of graphical models that can 0222 handle imprecision in probability values. The paper first reviews basic concepts 0223 and presents a brief historical account of the field. The main characteristics 0224 of the credal network model are then discussed, as this model has received 0225 considerable attention in the literature.}, 0226 author = {Fabio Gagliardi Cozman}, 0227 doi = {10.1016/j.ijar.2004.10.003}, 0228 issn = {0888-613X}, 0229 journal = {International Journal of Approximate Reasoning}, 0230 keywords = {Credal network; Graphical models; Sets of probability distributions; imprecise probability}, 0231 localfile = {article/Cozman-2005-graphical.pdf}, 0232 number = {2-3}, 0233 pages = {167–184}, 0234 title = {Graphical models for imprecise probabilities}, 0235 volume = {39}, 0236 year = {2005} 0237 } 0238 0239 @book{Liu-2007-uncertainty-theory, 0240 author = {Baoding Liu}, 0241 edition = {3}, 0242 title = {Uncertainty Theory}, 0243 year = {2007} 0244 } 0245 0246 @article{Ha-etal-1998, 0247 author = {Vu A. Ha and AnHai Doan and Van H. Vu and Peter Haddawy}, 0248 doi = {10.1023/A:1018936829318}, 0249 journal = {Annals of Mathematics and Artificial Intelligence}, 0250 localfile = {article/Ha-etal-1998.pdf}, 0251 pages = {1–21}, 0252 title = {Geometric foundations for interval-based probabilities}, 0253 volume = {24}, 0254 year = {1998} 0255 } 0256 0257 @phdthesis{Augustin-1998-phdthesis-parts, 0258 annote = {Extracts}, 0259 author = {Thomas Augustin}, 0260 isbn = {978-3-52511411-7}, 0261 school = {LMU München}, 0262 title = {Optimale Tests bei Intervallwahrscheinlichkeit}, 0263 year = {1998} 0264 } 0265 0266 @article{Daboni-1975, 0267 author = {Luciano Daboni}, 0268 journal = {Rendiconti di matematica}, 0269 localfile = {article/Daboni-1975.pdf}, 0270 pages = {399–412}, 0271 title = {Caratterizzatione delle successioni (funzioni) completamente monotone in termini di rappresentabilià delle funzioni di sopravvivenza di particolari intervalli scambiabli tra successi (arrivi) contigui}, 0272 volume = {8}, 0273 year = {1975} 0274 } 0275 0276 @article{Zaffalon-2002-ncc, 0277 abstract = {Convex sets of probability distributions are also called 0278 credal sets. They generalize probability theory by relaxing the requirement that 0279 probability values be precise. Classification, i.e. assigning class labels to 0280 instances described by a set of attributes, is an important domain of 0281 application of Bayesian methods, where the naive Bayes classifier has a 0282 surprisingly good performance. This paper proposes a new method of 0283 classification which involves extending the naive Bayes classifier to credal 0284 sets. Exact and effective solution procedures for naive credal classification 0285 are derived, and the related dominance criteria are discussed. Credal 0286 classiffcation appears as a new method, based on more realistic assumptions and 0287 in the direction of more reliable inferences.}, 0288 annote = {ook op papier}, 0289 author = {Marco Zaffalon}, 0290 doi = {10.1016/S0378-3758(01)00201-4}, 0291 journal = {Journal of Statistical Planning and Inference}, 0292 keywords = {Classification; Credal sets; Imprecise probabilities; Naive Bayes classifier; Pattern recognition}, 0293 localfile = {article/Zaffalon-2002-ncc.pdf}, 0294 number = {1}, 0295 pages = {5–21}, 0296 publisher = {Elsevier}, 0297 title = {The naive credal classifier}, 0298 volume = {105}, 0299 year = {2002} 0300 } 0301 0302 @article{Zaffalon-2005-environmental, 0303 abstract = {Classifiers that aim at doing credible predictions should 0304 rely on carefully elicited prior knowledge. Often this is not available so they 0305 should start learning from data in condition of near-ignorance. This paper shows 0306 empirically, on an agricultural data set, that established methods of 0307 classification do not always adhere to this principle. Traditional ways to 0308 represent prior ignorance are shown to have an overwhelming weight compared to 0309 the information in the data, producing overconfident predictions. This point is 0310 crucial for problems, such as environmental ones, where prior knowledge is often 0311 scarce and even the data may not be known precisely. Credal classification, and 0312 in particular the naive credal classifier, is proposed as more faithful ways to 0313 cope with the ignorance problem. With credal classification, conditions of 0314 ignorance may limit the power of the inferences, not the credibility of the 0315 predictions.}, 0316 author = {Marco Zaffalon}, 0317 doi = {10.1016/j.envsoft.2004.10.006}, 0318 journal = {Environmental Modelling \& Software}, 0319 number = {8}, 0320 pages = {1003–1012}, 0321 title = {Credible classification for environmental problems}, 0322 volume = {20}, 0323 year = {2005} 0324 } 0325 0326 @book{Kuznetsov-1991, 0327 address = {Moscow}, 0328 author = {Kuznetsov}, 0329 title = {No Title}, 0330 year = {1991} 0331 } 0332 0333 @book{Zabell-2005, 0334 address = {Cambridge, United Kingdom}, 0335 author = {Sandy L. Zabell}, 0336 publisher = {Cambridge University Press}, 0337 series = {Cambridge Studies in Probability, Induction, and Decision Theory}, 0338 title = {Symmetry and Its Discontents: Essay on the History of Inductive Probability}, 0339 year = {2005} 0340 } 0341 0342 @article{Combarro-Miranda-2008-polytope, 0343 abstract = {In this paper we deal with the problem of studying the 0344 structure of the polytope of non-additive measures for finite referential sets. 0345 We give a necessary and sufficient condition for two extreme points of this 0346 polytope to be adjacent. We also show that it is possible to find out in 0347 polynomial time whether two vertices are adjacent. These results can be extended 0348 to the polytope given by the convex hull of monotone Boolean functions. We also 0349 give some results about the facets and edges of the polytope of non-additive 0350 measures; we prove that the diameter of the polytope is 3 for referentials of 0351 three elements or more. Finally, we show that the polytope is combinatorial and 0352 study the corresponding properties; more concretely, we show that the graph of 0353 non-additive measures is Hamilton connected if the cardinality of the 0354 referential set is not 2.}, 0355 author = {Elías F. Combarro and Pedro Miranda}, 0356 doi = {10.1016/j.fss.2007.12.021}, 0357 journal = {Fuzzy Sets and Systems}, 0358 keywords = {Adjacency; Combinatorial polytopes; Complexity; Diameter; Monotone Boolean functions; Non-additive measures; Stack filters}, 0359 localfile = {article/Combarro-Miranda-2008-polytope.pdf}, 0360 number = {16}, 0361 pages = {2145–2162}, 0362 title = {On the polytope of non-additive measures}, 0363 url = {http://www.sciencedirect.com/science/article/B6V05-4RM881N-1/1/385e96ea2df064e7 0364 ab875367eafbf9f9}, 0365 volume = {159}, 0366 year = {2008} 0367 } 0368 0369 @article{Tatcher-1964, 0370 abstract = {Given the number of successes in a random sample, prediction 0371 limits can be determined for the number which will be observed in a second 0372 sample, in a way which does not depend on any assumption or inference about the 0373 unknown proportion in the population. Such "confidence limits" for the 0374 prediction are found to correspond to Bayesian solutions based on two particular 0375 prior distributions, and are related to Laplace's rule of succession. The 0376 results suggest a possible type of "prediction strategy".}, 0377 author = {A. R. Thatcher}, 0378 journal = {Journal of the Royal Statistical Society. Series B (Methodological)}, 0379 localfile = {article/Tatcher-1964.pdf}, 0380 number = {2}, 0381 pages = {176–210}, 0382 title = {Relationships between Bayesian and confidence limits for predictions}, 0383 url = {http://www.jstor.org/stable/2984417}, 0384 volume = {26}, 0385 year = {1964} 0386 } 0387 0388 @article{Aughenbaugh-Herrmann-2009, 0389 abstract = {This paper considers the problem of choosing between an 0390 existing component whose reliability is well established and a new component 0391 that has an unknown reliability. In some scenarios, the designer may have some 0392 initial beliefs about the new component's reliability. The designer may also 0393 have the opportunity to obtain more information and to update these beliefs. 0394 Then, based on these updated beliefs, the designer must make a decision between 0395 the two components. This paper examines the statistical approaches for updating 0396 reliability assessments and the decision policy that the designer uses. We 0397 consider four statistical approaches for modeling the uncertainty about the new 0398 component and updating assessments of its reliability: A classical approach, a 0399 precise Bayesian approach, a robust Bayesian approach, and an imprecise 0400 probability approach. The paper investigates the impact of different approaches 0401 on the decision between the components and compares them. In particular, given 0402 that the test results are random, the paper considers the likelihood of making a 0403 correct decision with each statistical approach under different scenarios of 0404 available information and true reliability. In this way, the emphasis is on 0405 practical comparisons of the policies rather than on philosophical arguments.}, 0406 author = {J. M. Aughenbaugh and J. W. Herrmann}, 0407 doi = {10.1080/15598608.2009.10411926}, 0408 issn = {1559-8608}, 0409 journal = {Journal of Statistical Theory and Practice}, 0410 keywords = {Bayesian statistics; Imprecise probabilities; Reliability assessment}, 0411 localfile = {article/Aughenbaugh-Herrmann-2009.pdf}, 0412 month = mar, 0413 number = {1}, 0414 pages = {289–303}, 0415 publisher = {Taylor \& Francis}, 0416 title = {Reliability-Based Decision Making: A Comparison of Statistical Approaches}, 0417 volume = {3}, 0418 year = {2009} 0419 } 0420 0421 @book{Handbook-Beta-2003, 0422 editor = {A. K. Gupta and S. Nadarajah}, 0423 publisher = {Marcel Dekker}, 0424 title = {Handbook of the Beta Distribution and its Applications}, 0425 year = {2003} 0426 } 0427 0428 @article{Kozine-Utkin-2002, 0429 abstract = {The requirement that precise state and transition 0430 probabilities be available is often not realistic because of cost, technical 0431 difficulties or the uniqueness of the situation under study. Expert judgements, 0432 generic data, heterogeneous and partial information on the occurrences of events 0433 may be sources of the probability assessments. All this source information 0434 cannot produce precise probabilities of interest without having to introduce 0435 drastic assumptions often of quite an arbitrary nature. in this paper the theory 0436 of interval-valued coherent previsions is employed to generalise discrete Markov 0437 chains to interval-valued probabilities. A general procedure of interval-valued 0438 probability elicitation is analysed as well. In addition, examples are 0439 provided.}, 0440 annote = {ook offprint}, 0441 author = {Igor O. Kozine and Lev V. Utkin}, 0442 doi = {10.1023/A:1014745904458}, 0443 journal = {Reliable Computing}, 0444 localfile = {article/Kozine-Utkin-2002.pdf}, 0445 pages = {97–113}, 0446 title = {Interval-Valued Finite Markov Chains}, 0447 volume = {8}, 0448 year = {2002} 0449 } 0450 0451 @inproceedings{Chrisman-1996, 0452 author = {Lonnie Chrisman}, 0453 booktitle = {Proceedings of the 12th Conference on Uncertainty in Artificial Intelligence}, 0454 publisher = {Morgan Kaufmann}, 0455 title = {Propagation of 2-Monotone Lower Probabilities on an Undirected Graph}, 0456 year = {1996} 0457 } 0458 0459 @article{DeFinetti-1933c, 0460 author = {Bruno de Finetti}, 0461 journal = {Atti della reale accadeamia nazionale dei Lincei, Rendiconti, Classe di Scienze fisiche, matematiche e naturali}, 0462 localfile = {article/DeFinetti-1933c.pdf}, 0463 pages = {279–284}, 0464 title = {Sulla legge di distribuzione dei valori in una successione di numeri aleatori equivalenti}, 0465 volume = {18}, 0466 year = {1933} 0467 } 0468 0469 @article{Gilbert-DeCooman-Kerre-2003, 0470 abstract = {Probability assessments of events are often linguistic in 0471 nature. We model them by means of possibilistic probabilities (a version of 0472 Zadeh's fuzzy probabilities with a behavioural interpretation) with a suitable 0473 shape for practical implementation (on a computer). Employing the tools of 0474 interval analysis and the theory of imprecise probabilities we argue that the 0475 verification of coherence for these possibilistic probabilities, the corrections 0476 of non-coherent to coherent possibilistic probabilities and their extension to 0477 other events and gambles can be performed by finite and exact algorithms. The 0478 model can furthermore be transformed into an imprecise first-order model, useful 0479 for decision making and statistical inference.}, 0480 annote = {ook op papier}, 0481 author = {L. Gilbert and Gert {De Cooman} and Etienne E. Kerre}, 0482 doi = {10.1007/s00500-002-0217-3}, 0483 journal = {Soft Computing}, 0484 keywords = {Fuzzy number; Fuzzy probability; Linguistic uncertainty; Lowest prevision; Possibility measure}, 0485 localfile = {article/Gilbert-DeCooman-Kerre-2003.pdf}, 0486 pages = {304–309}, 0487 title = {Practical implementation of possibilistic probability mass functions}, 0488 volume = {7}, 0489 year = {2003} 0490 } 0491 0492 @article{DeFinetti-1933a, 0493 author = {Bruno de Finetti}, 0494 journal = {Atti della reale accadeamia nazionale dei Lincei, Rendiconti, Classe di Scienze fisiche, matematiche e naturali}, 0495 localfile = {article/DeFinetti-1933a.pdf}, 0496 pages = {279–284}, 0497 title = {Classi di numeri aleatori equivalenti}, 0498 volume = {18}, 0499 year = {1933} 0500 } 0501 0502 @article{Munch-Krogh-2006, 0503 abstract = {BACKGROUND: The number of sequenced eukaryotic genomes is 0504 rapidly increasing. This means that over time it will be hard to keep supplying 0505 customised gene finders for each genome. This calls for procedures to 0506 automatically generate species-specific gene finders and to re-train them as the 0507 quantity and quality of reliable gene annotation grows. RESULTS: We present a 0508 procedure, Agene, that automatically generates a species-specific gene predictor 0509 from a set of reliable mRNA sequences and a genome. We apply a Hidden Markov 0510 model (HMM) that implements explicit length distribution modelling for all gene 0511 structure blocks using acyclic discrete phase type distributions. The state 0512 structure of the each HMM is generated dynamically from an array of sub-models 0513 to include only gene features represented in the training set. CONCLUSION: 0514 Acyclic discrete phase type distributions are well suited to model sequence 0515 length distributions. The performance of each individual gene predictor on each 0516 individual genome is comparable to the best of the manually optimised 0517 species-specific gene finders. It is shown that species-specific gene finders 0518 are superior to gene finders trained on other species.}, 0519 author = {Kasper Munch and Anders Krogh}, 0520 doi = {10.1186/1471-2105-7-263}, 0521 issn = {1471-2105}, 0522 journal = {BMC Bioinformatics}, 0523 localfile = {article/Munch-Krogh-2006.pdf}, 0524 number = {1}, 0525 pages = {263}, 0526 publisher = {BioMed Central Ltd}, 0527 title = {Automatic generation of gene finders for eukaryotic species}, 0528 volume = {7}, 0529 year = {2006} 0530 } 0531 0532 @article{Basu-Pereira-1983b, 0533 abstract = {The theory of conditional independence is explained and the 0534 relations between ancillarity, sufficiency and statistical independence are 0535 discussed in depth. Some related concepts like specific sufficiency, bounded 0536 completeness, and splitting sets are also studied in some details by using the 0537 language of conditional independence.}, 0538 annote = {ook op papier}, 0539 author = {D. Basu and Carlos A. B. Pereira}, 0540 journal = {Sankhya Series A}, 0541 keywords = {(strong) identification; Conditional independence; Markov property; ancillarity; measuable separability; specific sufficiency; splitting sets; sufficiency; variation independence}, 0542 localfile = {article/Basu-Pereira-1983b.pdf}, 0543 number = {3}, 0544 pages = {324–337}, 0545 title = {Conditional independence in statistics}, 0546 url = {http://www.jstor.org/stable/25050444}, 0547 volume = {45}, 0548 year = {1983} 0549 } 0550 0551 @article{Klee-1951, 0552 author = {Victor L. Jr. Klee}, 0553 doi = {10.1215/S0012-7094-51-01835-2}, 0554 journal = {Duke Mathematical Journal}, 0555 number = {2}, 0556 pages = {443–466}, 0557 title = {Convex sets in linear spaces}, 0558 volume = {18}, 0559 year = {1951} 0560 } 0561 0562 @article{Miranda-Grabisch-Gil-2002, 0563 archiveprefix = {arXiv}, 0564 arxivid = {0804.2642}, 0565 author = {Pedro Miranda and Michel Grabisch and Pedro Gil}, 0566 doi = {10.1142/S0218488502001867}, 0567 eprint = {0804.2642}, 0568 journal = {International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems}, 0569 localfile = {article/Miranda-Grabisch-Gil-2002.pdf}, 0570 number = {Supplementary Issue 1}, 0571 pages = {105–123}, 0572 title = {p-Symmetric fuzzy measures}, 0573 volume = {10}, 0574 year = {2002} 0575 } 0576 0577 @incollection{VanDorp-Mazzuchi-2003, 0578 author = {J. René {Van Dorp} and Thomas A. Mazzuchi}, 0579 booktitle = {Handbook of the Beta Distribution and its Applications}, 0580 editor = {A. K. Gupta and S. Nadarajah}, 0581 localfile = {inbook/VanDorp-Mazzuchi-2003.pdf}, 0582 pages = {283–316}, 0583 publisher = {Marcel Dekker}, 0584 title = {Parameter Specification of the Beta Distribution and its Dirichlet Extensions Utilizing Quantiles}, 0585 year = {2003} 0586 } 0587 0588 @article{Fodor-Marichal-Roubens-1995, 0589 author = {Janos Fodor and Jean-Luc Marichal and Marc Roubens}, 0590 journal = {IEEE Transactions on Fuzzy Systems}, 0591 localfile = {article/Fodor-Marichal-Roubens-1995.pdf}, 0592 number = {2}, 0593 pages = {236–240}, 0594 title = {Characterization of the Ordered Weighted Averaging Operators}, 0595 volume = {3}, 0596 year = {1995} 0597 } 0598 0599 @article{Pericchi-Walley-1991, 0600 author = {Luis Raúl Pericchi and Peter Walley}, 0601 journal = {International Statistical Review}, 0602 localfile = {article/Pericchi-Walley-1991.pdf}, 0603 number = {1}, 0604 pages = {1–23}, 0605 title = {Robust Bayesian credible intervals and prior ignorance}, 0606 url = {http://www.jstor.org/stable/1403571}, 0607 volume = {58}, 0608 year = {1991} 0609 } 0610 0611 @article{Fishburn-1980, 0612 abstract = {Stochastic dominance orders of all finite degrees are 0613 defined on the set of distribution functions on the nonnegative real numbers in 0614 terms of integrals of the distributions. It is proved that if F strictly 0615 nth-degree stochastically dominates G, and if the moments of F and G through 0616 order n are finite with $\mu \_{F}^{k}-∈t x^{k}dF(x)$, then $(\mu 0617 \_{F}^{1},…,\mu \_{F}^{n})\neq (\mu \_{G}^{n},…,\mu \_{G}^{n})$ and 0618 $(-1)^{k-1}\mu \_{F}^{k}>(-1)^{k-1}\mu \_{G}^{k}$ for the smallest k for which 0619 $\mu \_{F}^{k}\neq \mu \_{G}^{k}$.}, 0620 author = {Peter C. Fishburn}, 0621 issn = {0364-765X}, 0622 journal = {Mathematics of Operations Research}, 0623 localfile = {article/Fishburn-1980.pdf}, 0624 number = {1}, 0625 pages = {94–100}, 0626 publisher = {INFORMS}, 0627 title = {Stochastic dominance and moments of distributions}, 0628 url = {http://www.jstor.org/stable/3689397}, 0629 volume = {5}, 0630 year = {1980} 0631 } 0632 0633 @article{Walley-1996-IDM, 0634 abstract = {A new method is proposed for making inferences from 0635 multinomial data in cases where there is no prior information. A paradigm is the 0636 problem of predicting the colour of the next marble to be drawn from a bag whose 0637 contents are (initially) completely unknown. In such problems we may be unable 0638 to formulate a sample space because we do not know what outcomes are possible. 0639 This suggests an invariance principle: inferences based on observations should 0640 not depend on the sample space in which the observations and future events of 0641 interest are represented. Objective Bayesian methods do not satisfy this 0642 principle. This paper describes a statistical model, called the imprecise 0643 Dirichlet model, for drawing coherent inferences from multinomial data. 0644 Inferences are expressed in terms of posterior upper and lower probabilities. 0645 The probabilities are initially vacuous, reflecting prior ignorance, but they 0646 become more precise as the number of observations increases. This model does 0647 satisfy the invariance principle. Two sets of data are analysed in detail. In 0648 the first example one red marble is observed in six drawings from a bag. 0649 Inferences from the imprecise Dirichlet model are compared with objective 0650 Bayesian and frequentist inferences. The second example is an analysis of data 0651 from medical trials which compared two treatments for cardiorespiratory failure 0652 in newborn babies. There are two problems: to draw conclusions about which 0653 treatment is more effective and to decide when the randomized trials should be 0654 terminated. This example shows how the imprecise Dirichlet model can be used to 0655 analyse data in the form of a contingency table.}, 0656 annote = {with discussion geannoteerde kopie}, 0657 author = {Peter Walley}, 0658 journal = {Journal of the Royal Statistical Society. Series B (Methodological)}, 0659 localfile = {article/Walley-1996-IDM.pdf}, 0660 number = {1}, 0661 pages = {3–57}, 0662 title = {Inferences from multinomial data: learning about a bag of marbles}, 0663 url = {http://www.jstor.org/stable/2346164}, 0664 volume = {58}, 0665 year = {1996} 0666 } 0667 0668 @article{Bushell-1986-Hilbert-metric, 0669 abstract = {The Cayley-Hilbert metric is defined for a real Banach space 0670 containing a closed cone. By restricting the domain of a particular type of 0671 positive nonlinear operator, the Banach contraction-mapping theorem is used to 0672 prove the existence of a unique fixed point of the operator with explicit upper 0673 and lower bounds. Applications to quasilinear elliptic partial differential 0674 equations and to matrix theory are considered.}, 0675 author = {P. J. Bushell}, 0676 doi = {10.1016/0024-3795(86)90319-8}, 0677 journal = {Linear Algebra and its Applications}, 0678 localfile = {article/Bushell-1986-Hilbert-metric.pdf}, 0679 pages = {271–280}, 0680 publisher = {Elsevier}, 0681 title = {The Cayley-Hilbert metric and positive operators}, 0682 volume = {84}, 0683 year = {1986} 0684 } 0685 0686 @misc{DeCooman-2004-summer, 0687 annote = {Slides voor inleidende presentatie SIPTA summer school}, 0688 author = {Gert {De Cooman}}, 0689 title = {Coherent lower and upper previsions (and their behavioural interpretation)}, 0690 year = {2004} 0691 } 0692 0693 @book{deFinetti-1992, 0694 author = {Bruno de Finetti}, 0695 editor = {Paola Monari and Daniela Cocchi}, 0696 publisher = {CLUEB, Bologna}, 0697 title = {Probabilità e Induzione – Induction and Probability}, 0698 url = {http://diglib.cib.unibo.it/diglib.php?inv=35&term_ptnum=1&format=jpg}, 0699 volume = {52}, 0700 year = {1992} 0701 } 0702 0703 @article{Bot-Lorenz-Wanka-2010, 0704 author = {Radu Ioan Bot and Nicole Lorenz and Gert Wanka}, 0705 doi = {10.4134/JKMS.2010.47.1.017}, 0706 journal = {Journal of The Korean Mathematical Society}, 0707 localfile = {article/Bot-Lorenz-Wanka-2010.pdf}, 0708 pages = {17–28}, 0709 title = {Duality for linear chance-constrained optimization problems}, 0710 volume = {47}, 0711 year = {2010} 0712 } 0713 0714 @book{Levi-1980, 0715 address = {London}, 0716 author = {Isaac Levi}, 0717 publisher = {MIT Press}, 0718 title = {The Enterprise of Knowledge}, 0719 year = {1980} 0720 } 0721 0722 @article{Lambrakis1969, 0723 author = {D. P. Lambrakis}, 0724 journal = {Journal of the Royal Statistical Society. Series B (Methodological)}, 0725 localfile = {article/Ericson-1969.pdf}, 0726 number = {2}, 0727 pages = {234–245}, 0728 title = {Experiments with mixtures: an alternative to the simplex-lattice design}, 0729 url = {http://www.jstor.org/stable/2984207}, 0730 volume = {31}, 0731 year = {1969} 0732 } 0733 0734 @article{Rosenthal-1995-Markov-rate, 0735 abstract = {This is an expository paper that presents various ideas 0736 related to nonasymptotic rates of convergence for Markov chains. Such rates are 0737 of great importance for stochastic algorithms that are widely used in statistics 0738 and in computer science. They also have applications to analysis of card 0739 shuffling and other areas.In this paper, we attempt to describe various 0740 mathematical techniques that have been used to bound such rates of convergence. 0741 In particular, we describe eigenvalue analysis, random walks on groups, 0742 coupling, and minorization conditions. Connections are made to modern areas of 0743 research wherever possible. Elements of linear algebra, probability theory, 0744 group theory, and measure theory are used, but efforts are made to keep the 0745 presentation elementary and accessible.}, 0746 author = {Jeffrey S. Rosenthal}, 0747 doi = {10.1137/1037083}, 0748 journal = {SIAM Review}, 0749 keywords = {Markov chain; coupling; eigenvalue; random walk on group}, 0750 localfile = {article/Rosenthal-1995-Markov-rate.pdf}, 0751 number = {3}, 0752 pages = {387–405}, 0753 title = {Convergence rates for Markov chains}, 0754 url = {http://www.jstor.org/stable/2132659}, 0755 volume = {37}, 0756 year = {1995} 0757 } 0758 0759 @misc{Doumont-2001-website, 0760 author = {Jean-luc Doumont}, 0761 title = {Designing Web sites}, 0762 year = {2001} 0763 } 0764 0765 @inproceedings{Capotorti-Zagoraiou-2006, 0766 address = {Paris}, 0767 author = {Andrea Capotorti and Maroussa Zagoraiou}, 0768 booktitle = {Proceedings of the Eleventh International Conference on Information Processing and Management of Uncertainty in Knowledge-based Systems}, 0769 title = {Implicit Degree of Support for Finite Lower-Upper Conditional Probabilities Extensions}, 0770 year = {2006} 0771 } 0772 0773 @article{Bloch-Watson-1967, 0774 abstract = {Lindley [6] studies the topic in our title. By using 0775 Fisher's conditional-Poisson approach to the multinomial and the logarithmic 0776 transformation of gamma variables to normality, he showed that linear contrasts 0777 in the logarithms of the cell probabilities $\theta$\_i are asymptotically 0778 jointly normal and suggested that the approximation can be improved by applying 0779 a "correction" to the sample. By studying the asymptotic series for the joint 0780 distribution in Section 2 an improved correction procedure is found below. A 0781 more detailed expansion is given in Section 3 for the distribution of a single 0782 contrast in the \log $\theta$\_i. In many problems a linear function of the 0783 $\theta$\_i is of interest. The exact distribution is obtained and is of a form 0784 familiar in the theory of serial correlation coefficients. A beta approximation 0785 is given. For three cells, a numerical example is given to show the merit of 0786 this approximation. A genetic linkage example is considered which requires the 0787 joint distribution of two linear functions of the $\theta$\_i. The exact joint 0788 distribution is found but is too involved for practical use. A normal 0789 approximation leads to Lindley's results [7].}, 0790 author = {Daniel A. Bloch and Geoffrey S. Watson}, 0791 journal = {The Annals of Mathematical Statistics}, 0792 localfile = {article/Bloch-Watson-1967.pdf}, 0793 number = {5}, 0794 pages = {1423–1435}, 0795 title = {A Bayesian study of the multinomial distribution}, 0796 url = {http://www.jstor.org/stable/2238958}, 0797 volume = {38}, 0798 year = {1967} 0799 } 0800 0801 @misc{Good-2003, 0802 author = {I. J. Good}, 0803 title = {The accumulation of imprecise weights of evidence}, 0804 year = {2003} 0805 } 0806 0807 @article{Zabell-1982, 0808 abstract = {How do Bayesians justify using conjugate priors on grounds 0809 other than mathematical convenience? In the 1920's the Cambridge philosopher 0810 William Ernest Johnson in effect characterized symmetric Dirichlet priors for 0811 multinomial sampling in terms of a natural and easily assessed subjective 0812 condition. Johnson's proof can be generalized to include asymmetric Dirichlet 0813 priors and those finitely exchangeable sequences with linear posterior 0814 expectation of success. Some interesting open problems that Johnson's result 0815 raises, and its historical and philosophical background, are also discussed.}, 0816 annote = {ook op papier}, 0817 author = {Sandy L. Zabell}, 0818 doi = {10.1214/aos}, 0819 journal = {The Annals of Statistics}, 0820 localfile = {article/Zabell-1982.pdf}, 0821 number = {4}, 0822 pages = {1091–1099}, 0823 publisher = {Institute of Mathematical Statistics}, 0824 title = {W. E. Johnson's “sufficientness” postulate}, 0825 volume = {10}, 0826 year = {1982} 0827 } 0828 0829 @article{Cifarelli-Regazzini-1996, 0830 abstract = {This paper summarizes the scientific activity of de Finetti 0831 in probability and statistics. It falls into three sections: Section 1 includes 0832 an essential biography of de Finetti and a survey of the basic features of the 0833 scientific milieu in which he took the first steps of his scientific career; 0834 Section 2 concerns de Finetti's work in probability: (a) foundations, (b) 0835 processes with independent increments, (c) sequences of exchangeable random 0836 variables, and (d) contributions which fall within other fields; Section 3 deals 0837 with de Finetti's contributions to statistics: (a) description of frequency 0838 distributions, (b) induction and statistics, (c) probability and induction, and 0839 (d) objectivistic schools and theory of decision. Many recent developments of de 0840 Finetti's work are mentioned here and briefly described.}, 0841 author = {Donato Michele Cifarelli and Eugenio Regazzini}, 0842 doi = {10.1214/ss}, 0843 journal = {Statistical Science}, 0844 keywords = {Associative mean; Bayes-Laplace paradigm; Bayesian nonparametric statistics; Glivenko-Cantelli theorem; completely additive probabilities; correlation and monotone dependence; exchangeable and partially exchangeable random var; finitely additive probabilities; gambler's ruin; infinitely decomposable laws; predictive inference; prevision; principle of coherence processes with independent; reasoning by induction; statistical decision; subjective probability; utility function}, 0845 localfile = {article/Cifarelli-Regazzini-1996.pdf}, 0846 number = {4}, 0847 pages = {253–282}, 0848 title = {De Finetti's Contribution to probability and Statistics}, 0849 volume = {11}, 0850 year = {1996} 0851 } 0852 0853 @proceedings{ISIPTA-2003, 0854 address = {Waterloo, Ontario, Canada}, 0855 booktitle = {ISIPTA '03: Proceedings of the Third International Symposium on Imprecise Probabilities and Their Applications}, 0856 editor = {Jean-Marc Bernard and Teddy Seidenfeld and Marco Zaffalon}, 0857 location = {Lugano, Switzerland}, 0858 publisher = {Carleton Scientific}, 0859 series = {Proceedings in Informatics}, 0860 title = {ISIPTA '03: Proceedings of the Third International Symposium on Imprecise Probabilities and Their Applications}, 0861 volume = {18}, 0862 year = {2003} 0863 } 0864 0865 @article{Rommelfanger-2004, 0866 abstract = {Classical mathematical programming models require 0867 well-defined coefficients and right hand sides. In order to avoid a non 0868 satisfying modeling usually a broad information gathering and processing is 0869 necessary. In case of real problems some model parameters can be only roughly 0870 estimated. While in case of classical models the vague data is replaced by 0871 "average data", fuzzy models offer the opportunity to model subjective 0872 imaginations of the decision maker as precisely as a decision maker will be able 0873 to describe it. Thus the risk of applying a wrong model of the reality and 0874 selecting solutions which do not reflect the real problem can be clearly 0875 reduced. The modeling of real problems by means of deterministic and stochastic 0876 models requires extensive information processing. On the other hand we know that 0877 an optimum solution is finally defined only by few restrictions. Especially in 0878 case of larger systems we notice afterwards that most of the information is 0879 useless. The dilemma of data processing is due to the fact that first we have to 0880 calculate the solution in order to define, whether the information must be 0881 well-defined or whether vague data may be sufficient. Based on multicriteria 0882 programming problems it should be demonstrated that the dilemma of data 0883 processing in case of real programming problems can be handled adequately by 0884 modeling them as fuzzy system combined with an interactive problem-solving. 0885 Describing the real problem by means of a fuzzy system first of all only the 0886 available information or such information which can be achieved easily will be 0887 considered. Then we try to develop an optimum solution. With reference to the 0888 cost-benefit relation further information can be gathered in order to describe 0889 the solution more precisely. Furthermore it should be pointed out that some 0890 interactive fuzzy solution algorithms, e.g. FULPAL provide the opportunity to 0891 solve mixed integer multicriteria programming models as well.}, 0892 author = {Heinrich Rommelfanger}, 0893 doi = {10.1007/s10700-004-4200-6}, 0894 issn = {1568-4539}, 0895 journal = {Fuzzy Optimization and Decision Making}, 0896 localfile = {article/Rommelfanger-2004.pdf}, 0897 pages = {295–309}, 0898 publisher = {Springer Netherlands}, 0899 title = {The Advantages of Fuzzy Optimization Models in Practical Use}, 0900 volume = {3}, 0901 year = {2004} 0902 } 0903 0904 @incollection{Mukerji-Tallon-2003, 0905 author = {Sujoy Mukerji and Jean-Marc Tallon}, 0906 booktitle = {Uncertainty in Economic Theory: A collection of essays in honor of David Schmeidler's 65th birthday}, 0907 editor = {I. Gilboa}, 0908 publisher = {Routledge}, 0909 title = {An overview of economic applications of David Schmeidler's models of decision making under uncertainty}, 0910 year = {2004} 0911 } 0912 0913 @article{Smith-1961, 0914 abstract = {It is suggested that the strength of a person's beliefs may 0915 be tested by finding at what odds he is prepared to bet on them. This leads to a 0916 system of numerical "medial personal probabilities" obeying the classical laws 0917 of probability. However, these do not have precisely defined values, but are 0918 contained within specified intervals. The appropriate method of inference is 0919 Bayes's Theorem. This leads to generally accepted statistical procedures in 0920 large samples, except that the "weight of evidence" and not significance level 0921 is the measure of conviction in a significance test. Under very general 0922 conditions decisions are made by maximizing expected utility.}, 0923 annote = {geannoteerde kopie op papier}, 0924 author = {Cedric A. B. Smith}, 0925 issn = {0035-9246}, 0926 journal = {Journal of the Royal Statistical Society. Series B (Methodological)}, 0927 localfile = {article/Smith-1961.pdf}, 0928 number = {1}, 0929 pages = {1–37}, 0930 publisher = {Blackwell Publishing for the Royal Statistical Society}, 0931 title = {Consistency in statistical inference and decision}, 0932 url = {http://www.jstor.org/stable/2983842}, 0933 volume = {23}, 0934 year = {1961} 0935 } 0936 0937 @book{Kemeny-Snell-1976-markov, 0938 address = {New York and Berlin and Heidelberg and Tokyo}, 0939 author = {John G. Kemeny and J. Laurie Snell}, 0940 edition = {2}, 0941 publisher = {Springer}, 0942 series = {Undergraduate Texts in Mathematics}, 0943 title = {Finite Markov Chains}, 0944 url = {http://books.google.com/books?id=0bTK5uWzbYwC}, 0945 year = {1976} 0946 } 0947 0948 @inproceedings{Lee-Varaiya-2000-sysensig, 0949 annote = {ook op papier}, 0950 author = {Edward A. Lee and Pravin Varaiya}, 0951 booktitle = {Proceedings of the First Signal Processing Workshop}, 0952 title = {Introducing signals and syetems – The Berkeley approach}, 0953 year = {2000} 0954 } 0955 0956 @article{Williams-1978, 0957 annote = {Review of Shafer-1976}, 0958 author = {Peter M. Williams}, 0959 journal = {The British Journal for the Philosophy of Science}, 0960 localfile = {article/Williams-1978.pdf}, 0961 number = {4}, 0962 pages = {375–387}, 0963 title = {On a new theory of epistemic probability}, 0964 url = {http://www.jstor.org/stable/687102}, 0965 volume = {29}, 0966 year = {1978} 0967 } 0968 0969 @article{Luce-VonWinterfeld-1994, 0970 abstract = {Descriptive and normative modeling of decision making under 0971 risk and uncertainty have grown apart over the past decade. Psychological models 0972 attempt to accommodate the numerous violations of rationality axioms, including 0973 independence and transitivity. Meanwhile, normatively oriented decision analysts 0974 continue to insist on the applied usefulness of the subjective expected utility 0975 (SEU) model. As this gap has widened, two facts have remained largely 0976 unobserved. First, most people in real situations attempt to behave in accord 0977 with the most basic rationality principles, even though they are likely to fail 0978 in more complex situations. Second, the SEU model is likely to provide 0979 consistent and rational answers to decision problems within a given problem 0980 structure, but may not be invariant across structures. Thus, people may be more 0981 rational than the psychological literature gives them credit for, and 0982 applications of the SEU model may be susceptible to some violations of 0983 invariance principles. This paper attempts to search out the common ground 0984 between the normative, descriptive, and prescriptive modeling by exploring three 0985 types of axioms concerning structural rationality, preference rationality, and 0986 quasi-rationality. Normatively the first two are mandatory and the last, 0987 suspect. Descriptively, all have been questioned, but often the inferences 0988 involved have confounded preference and structural rationality. We propose a 0989 prescriptive view that entails full compliance with preference rationality, 0990 modifications of structural rationality, and acceptance of quasi-rationality to 0991 the extent of granting a primary role to the status quo and the decomposition of 0992 decision problems into gains and losses.}, 0993 author = {R. Duncan Luce and Detlof von Winterfeldt}, 0994 doi = {10.1287/mnsc.40.2.263}, 0995 journal = {Management Science}, 0996 keywords = {Decision Analysis; Prescriptive Utility; Rank-Dependent Utility; Sign-Dependent Utility}, 0997 localfile = {article/Luce-VonWinterfeld-1994.pdf}, 0998 number = {2}, 0999 pages = {263–279}, 1000 title = {What common ground exists for descriptive, prescriptive, and normative utility theories?}, 1001 url = {http://www.jstor.org/stable/2632765}, 1002 volume = {40}, 1003 year = {1994} 1004 } 1005 1006 @article{Whittle-1955, 1007 abstract = {An exact formula (8) is derived for the probability 1008 distribution of an observed set of transition totals. This expression furnishes 1009 asymptotic expressions for the likelihood (24), for the covariances of 1010 transition totals (27), and for the distribution of Bartlett's goodness-of-fit 1011 statistic (31). Formulae are also derived for the expectations of some sample 1012 functions related to the factorial moments of the transition totals (34) and for 1013 the lower moments of the estimated transition probabilities (42), (44). It is 1014 shown that the Markov chain has properties similar to those of a set of 1015 independent multinomial distributions.}, 1016 annote = {geannoteerde kopie}, 1017 author = {Peter Whittle}, 1018 journal = {Journal of the Royal Statistical Society. Series B (Methodological)}, 1019 localfile = {article/Whittle-1955.pdf}, 1020 number = {2}, 1021 pages = {235–242}, 1022 title = {Some distribution and moment formulae for the Markov chain}, 1023 url = {http://www.jstor.org/stable/2983957}, 1024 volume = {17}, 1025 year = {1955} 1026 } 1027 1028 @techreport{Deshpande-Karypis-2000, 1029 author = {Mukund Deshpande and George Karypis}, 1030 institution = {University of Minnesota, Department of Computer Science}, 1031 number = {00-056}, 1032 title = {Selective Markov Models for Predicting Web-Page Accesses}, 1033 year = {2000} 1034 } 1035 1036 @phdthesis{Degrauwe-2007-PhD, 1037 author = {Daan Degrauwe}, 1038 school = {Katholieke Universiteit Leuven}, 1039 title = {Uncertainty propagation in structural analysis by fuzzy numbers}, 1040 year = {2007} 1041 } 1042 1043 @article{GuitierrezPena-Smith-1995, 1044 annote = {met errata, ook op papier}, 1045 author = {Eduardo Gutiérrez-Peña and Adrian F. M. Smith}, 1046 journal = {Journal of the American Statistical Association}, 1047 keywords = {Bayesian inference; Conjugate prior; Jeffreys's prior; Quadratic variance function}, 1048 localfile = {article/GutierrezPena-Smith-1995.pdf}, 1049 number = {432}, 1050 pages = {1347–1356}, 1051 title = {Conjugate parameterizations for natural exponential families}, 1052 url = {http://www.jstor.org/stable/2291525}, 1053 volume = {90}, 1054 year = {1995} 1055 } 1056 1057 @article{Krein-Milman-1940, 1058 author = {M. Krein and D. Milman}, 1059 journal = {Studia Mathematica}, 1060 localfile = {article/Krein-Milman-1940.pdf}, 1061 pages = {133–138}, 1062 title = {On extreme points of regular convex sets}, 1063 volume = {9}, 1064 year = {1940} 1065 } 1066 1067 @article{Tukey-1986-sunset, 1068 author = {John W. Tukey}, 1069 journal = {The American Statistician}, 1070 localfile = {article/Tukey-1986-sunset.pdf}, 1071 number = {1}, 1072 pages = {72–76}, 1073 title = {Sunset salvo}, 1074 url = {http://www.jstor.org/stable/2683137}, 1075 volume = {40}, 1076 year = {1986} 1077 } 1078 1079 @article{Hammer-1955, 1080 author = {Preston C. Hammer}, 1081 doi = {10.1215/S0012-7094-55-02209-2}, 1082 journal = {Duke Mathematical Journal}, 1083 localfile = {article/Hammer-1955.pdf}, 1084 number = {1}, 1085 pages = {103–106}, 1086 publisher = {Duke University Press}, 1087 title = {Maximal convex sets}, 1088 volume = {22}, 1089 year = {1955} 1090 } 1091 1092 @proceedings{Cowles-1951, 1093 booktitle = {Activity analysis of production and allocation}, 1094 editor = {Tjalling C. Koopmans}, 1095 number = {13}, 1096 organization = {Cowles Commission for Research in Economics}, 1097 series = {Cowles Commission Monographs}, 1098 title = {Activity analysis of production and allocation}, 1099 year = {1951} 1100 } 1101 1102 @article{Consonni-Veronese-GutierrezPena-2004, 1103 abstract = {Reference analysis is one of the most successful general 1104 methods to derive noninformative prior distributions. In practice, however, 1105 reference priors are often difficult to obtain. Recently developed theory for 1106 conditionally reducible natural exponential families identifies an attractive 1107 reparameterization which allows one, among other things, to construct an 1108 enriched conjugate prior. In this paper, under the assumption that the variance 1109 function is simple quadratic, the order-invariant group reference prior for the 1110 above parameter is found. Furthermore, group reference priors for the mean- and 1111 natural parameter of the families are obtained. A brief discussion of the 1112 frequentist coverage properties is also presented. The theory is illustrated for 1113 the multinomial and negative-multinomial family. Posterior computations are 1114 especially straightforward due to the fact that the resulting reference 1115 distributions belong to the corresponding enriched conjugate family. A 1116 substantive application of the theory relates to the construction of reference 1117 priors for the Bayesian analysis of two-way contingency tables with respect to 1118 two alternative parameterizations.}, 1119 author = {Guido Consonni and Piero Veronese and Eduardo Gutiérrez-Peña}, 1120 doi = {10.1016/S0047-259X(03)00095-2}, 1121 journal = {Journal of Multivariate Analysis}, 1122 keywords = {Bayesian inference; Contingency table; Enriched conjugate prior; Multinomial family; Negative-multinomial family; Noninformative prior; conditional reducibility}, 1123 localfile = {article/Consonni-Veronese-GutierrezPena-2004.pdf}, 1124 number = {2}, 1125 pages = {335–364}, 1126 publisher = {Elsevier}, 1127 title = {Reference priors for exponential families with simple quadratic variance function}, 1128 volume = {88}, 1129 year = {2004} 1130 } 1131 1132 @article{Quaeghebeur-DeCooman-2009-idmgames, 1133 author = {Erik Quaeghebeur and Gert {De Cooman}}, 1134 doi = {10.1016/j.ijar.2008.03.012}, 1135 journal = {International Journal of Approximate Reasoning}, 1136 pages = {243–256}, 1137 title = {Learning in games using the imprecise Dirichlet-model}, 1138 volume = {50}, 1139 year = {2009} 1140 } 1141 1142 @techreport{Ferson-et-al-2002, 1143 annote = {unabridged version, with corrections, printed in 2003}, 1144 author = {Scott Ferson and Vladik Kreinovich and Lev Ginzburg and Davis S. Myers and Kari Sentz}, 1145 institution = {Sandia National Laboratories}, 1146 number = {SAND2002-4015}, 1147 title = {Constructing probability boxes and Dempster-Shafer structures}, 1148 year = {2002} 1149 } 1150 1151 @article{Wagner-1999-two-envelope, 1152 annote = {op papier in Wagnerbundel}, 1153 author = {Carl G. Wagner}, 1154 journal = {Erkenntnis}, 1155 pages = {233–241}, 1156 title = {Misadventures in conditional expectation: the two-envelope problem}, 1157 volume = {51}, 1158 year = {1999} 1159 } 1160 1161 @article{Augustin-2005, 1162 abstract = {Dempster-Shafer theory allows to construct belief functions 1163 from (precise) basic probability assignments. The present paper extends this 1164 idea substantially. By considering sets of basic probability assignments, an 1165 appealing constructive approach to general interval probability is achieved, 1166 which allows for a very flexible modelling of uncertain knowledge.}, 1167 author = {Thomas Augustin}, 1168 doi = {10.1080/03081070500190839}, 1169 journal = {International Journal of General Systems}, 1170 keywords = {Basic probability assignment; Belief function; Dempster–Shafer theory; Imprecise probabilities; Interval probability; Linear partial information}, 1171 localfile = {article/Augustin-2005.pdf}, 1172 number = {4}, 1173 pages = {451–463}, 1174 title = {Generalized basic probability assignments}, 1175 volume = {34}, 1176 year = {2005} 1177 } 1178 1179 @article{Pearl-1988-intervals, 1180 abstract = {The apparent failure of individual probabilistic expressions 1181 to distinguish between uncertainty and ignorance, and between certainty and 1182 confidence, have swayed researchers to seek alternative formalisms, where 1183 confidence measures are provided explicit notation. This paper summarizes how a 1184 causal networks formulation of probabilities facilitates the representation of 1185 confidence measures as an integral part of a knowledge system that does not 1186 require the use of higher order probabilities. We also examine whether 1187 Dempster-Shafer intervals represent confidence about probabilities.}, 1188 author = {Judea Pearl}, 1189 doi = {10.1016/0888-613X(88)90117-X}, 1190 issn = {0888-613X}, 1191 journal = {International Journal of Approximate Reasoning}, 1192 keywords = {Dempster-Shafer theory; ca; interval probability}, 1193 localfile = {article/Pearl-1988-intervals.pdf}, 1194 number = {3}, 1195 pages = {211–216}, 1196 publisher = {Elsevier}, 1197 title = {On probability intervals}, 1198 volume = {2}, 1199 year = {1988} 1200 } 1201 1202 @article{DeFinetti-1933b, 1203 author = {Bruno de Finetti}, 1204 journal = {Atti della reale accadeamia nazionale dei Lincei, Rendiconti, Classe di Scienze fisiche, matematiche e naturali}, 1205 localfile = {article/DeFinetti-1933b.pdf}, 1206 pages = {203–207}, 1207 title = {La legge dei grandi numeri nel caso dei numeri aleatori equivalenti}, 1208 volume = {18}, 1209 year = {1933} 1210 } 1211 1212 @article{Walley-1997-bounded, 1213 abstract = {A new method is proposed for drawing coherent statistical 1214 inferences about a real-valued parameter in problems where there is little or no 1215 prior information. Prior ignorance about the parameter is modelled by the set of 1216 all continuous probability density functions for which the derivative of the 1217 log-density is bounded by a positive constant. This set is 1218 translation-invariant, it contains density functions with a wide variety of 1219 shapes and tail behaviour, and it generates prior probabilities that are highly 1220 imprecise. Statistical inferences can be calculated by solving a simple type of 1221 optimal control problem whose general solution is characterized. Detailed 1222 results are given for the problems of calculating posterior upper and lower 1223 means, variances, distribution functions and probabilities of intervals. In 1224 general, posterior upper and lower expectations are achieved by prior density 1225 functions that are piecewise exponential. The results are illustrated by normal 1226 and binomial examples}, 1227 author = {Peter Walley}, 1228 doi = {10.1111/1467-9469.00075}, 1229 journal = {Scandinavian Journal of Statistics}, 1230 localfile = {article/Walley-1997-bounded.pdf}, 1231 number = {4}, 1232 pages = {463–483}, 1233 title = {A Bounded Derivative model for Prior Ignorance about a Real-valued Parameter}, 1234 volume = {24}, 1235 year = {1997} 1236 } 1237 1238 @incollection{Piatti-et-al-2010-CNtutorial, 1239 address = {New York}, 1240 annote = {ook op papier}, 1241 author = {Alberto Piatti and Alessandro Antonucci and Marco Zaffalon}, 1242 booktitle = {Advances in Mathematics Research}, 1243 editor = {Albert R. Baswell}, 1244 publisher = {Nova Publishers}, 1245 title = {Building Knowledge-Based Systems by Credal Networks: A Tutorial}, 1246 volume = {11}, 1247 year = {2010} 1248 } 1249 1250 @techreport{Walley-Bernard-1999, 1251 annote = {geannoteerde kopie}, 1252 author = {Peter Walley and Jean-Marc Bernard}, 1253 institution = {Université de Paris 8}, 1254 number = {CAF-9901}, 1255 title = {Imprecise Probabilistic Prediction for Categorical Data}, 1256 year = {1999} 1257 } 1258 1259 @book{DeFinetti-1972, 1260 annote = {geringde kopie}, 1261 author = {Bruno de Finetti}, 1262 publisher = {John Wiley \& Sons}, 1263 title = {Probability, Induction and Statistics (The art of guessing)}, 1264 year = {1972} 1265 } 1266 1267 @article{Suppes-1974, 1268 abstract = {This paper criticizes some of the claims of the standard 1269 theories of subjective probability. The criticisms are especially oriented 1270 toward the structural axioms that cannot be regarded as axioms of pure 1271 rationality and the general results that yield exact measurement of subjective 1272 probabilities. Qualitative axioms for upper and lower probability are introduced 1273 to provide a theory of inexact measurement of subjective probability. Only minor 1274 modifications of de Finetti's qualitative axioms yield the desired theory. The 1275 paper concludes with a comparison of the measurement of belief to the 1276 measurement results characteristic of Euclidean geometry, and also examines 1277 briefly some possibilities for using learning models as simplified abstract 1278 processes for constructing belief.}, 1279 author = {Patrick Suppes}, 1280 issn = {0035-9246}, 1281 journal = {Journal of the Royal Statistical Society. Series B (Methodological)}, 1282 keywords = {belief; lower probability; measurement; upper probability}, 1283 localfile = {article/Suppes-1974.pdf}, 1284 number = {2}, 1285 pages = {160–191}, 1286 title = {The measurement of belief}, 1287 url = {http://www.jstor.org/stable/2984811}, 1288 volume = {36}, 1289 year = {1974} 1290 } 1291 1292 @article{Revuz-1956, 1293 author = {André Revuz}, 1294 journal = {Annales de l'Institut Fourier}, 1295 localfile = {article/Revuz-1956.pdf}, 1296 pages = {187–269}, 1297 title = {Fonctions croissantes et mesures sur les espaces topologiques ordonnés}, 1298 url = {http://www.numdam.org/item?id=AIF_1956__6__187_0}, 1299 volume = {6}, 1300 year = {1956} 1301 } 1302 1303 @phdthesis{Davison-2002, 1304 abstract = {User-perceived retrieval latencies in the World Wide Web can 1305 be improved by preloading a local cache with resources likely to be accessed. A 1306 user requesting content that can be served by the cache is able to avoid the 1307 delays inherent in the Web, such as congested networks and slow servers. The 1308 difficulty, then, is to determine what content to prefetch into the cache. This 1309 work explores machine learning algorithms for user sequence prediction, both in 1310 general and speciffically for sequences of Web requests. We also consider 1311 information retrieval techniques to allow the use of the content of Web pages to 1312 help predict future requests. Although history-based mechanisms can provide 1313 strong performance in predicting future requests, performance can be improved by 1314 including predictions from additional sources. While past researchers have used 1315 a variety of techniques for evaluating caching algorithms and systems, most of 1316 those methods were not applicable to the evaluation of prefetching algorithms or 1317 systems. Therefore, two new mechanisms for evaluation are introduced. The first 1318 is a detailed trace-based simulator, built from scratch, that estimates 1319 client-side response times in a simulated network of clients, caches, and Web 1320 servers with various connectivity. This simulator is then used to evaluate 1321 various prefetching approaches. The second evaluation method presented is a 1322 novel architecture to simultaneously evaluate multiple proxy caches in a live 1323 network, which we introduce, implement, and demonstrate through experiments. The 1324 simulator is appropriate for evaluation of algorithms and research ideas, while 1325 simultaneous proxy evaluation is ideally suited to implemented systems. We also 1326 consider the present and the future ofWeb prefetching, nding that changes to the 1327 HTTP standard will be required in order for Web prefetching to become 1328 commonplace.}, 1329 author = {Brian Douglas Davison}, 1330 school = {Rutgers, The State University of New Jersey}, 1331 title = {The design and evaluation of web prefetching and caching techniques}, 1332 year = {2002} 1333 } 1334 1335 @book{Fiedler-etal-2006-inexactLP, 1336 author = {M. Fiedler and Jiri Nedoma and Jaroslav Ramík and Jiri Rohn and Karel Zimmermann}, 1337 publisher = {Springer}, 1338 title = {Linear Optimization Problems with Inexact Data}, 1339 url = {http://www.nsc.ru/interval/Library/InteBooks/InexactLP.pdf}, 1340 year = {2006} 1341 } 1342 1343 @inbook{Avis-2000-lrs, 1344 author = {David Avis}, 1345 booktitle = {Polytopes - Combinatorics and Computation}, 1346 editor = {Gil Kalai and Günther Ziegler}, 1347 pages = {177–198}, 1348 publisher = {Birkhäuser}, 1349 series = {DMV Seminar}, 1350 title = {lrs: A Revised Implementation of the Reverse Search Vertex Enumeration Algorithm}, 1351 url = {http://cgm.cs.mcgill.ca/~avis/C/lrs.html}, 1352 volume = {29}, 1353 year = {2000} 1354 } 1355 1356 @article{Zimmermann-1975, 1357 abstract = {The concept of fuzzy sets is presented as a new tool for the 1358 formulation and solution of systems and decision problems which contain fuzzy 1359 components or fuzzy relationships. After a brief description of the basic theory 1360 of fuzzy sets, implications to systems theory and decision making are indicated. 1361 Fuzzy set theory is then applied to fuzzy linear programming problems and it is 1362 shown how fuzzy linear programming problems can be solved without increasing the 1363 computational effort. Some critical remarks concerning the presently existing 1364 axioms and necessary future research efforts conclude this introductionary 1365 paper.}, 1366 author = {Hans-Jürgen Zimmermann}, 1367 doi = {10.1080/03081077508960870}, 1368 journal = {International Journal of General Systems}, 1369 number = {1}, 1370 title = {Description and optimization of fuzzy systems}, 1371 volume = {2}, 1372 year = {1975} 1373 } 1374 1375 @article{Klee-1956, 1376 author = {Victor L. Jr. Klee}, 1377 journal = {Mathematica Scandinavica}, 1378 localfile = {article/Klee-1956.pdf}, 1379 pages = {54–64}, 1380 title = {The structure of semispaces}, 1381 url = {http://www.mscand.dk/article.php?id=1449}, 1382 volume = {4}, 1383 year = {1956} 1384 } 1385 1386 @article{DeCooman-2005-order, 1387 annote = {reprint}, 1388 author = {Gert {De Cooman}}, 1389 doi = {10.1007/s10472-005-9006-x}, 1390 journal = {Annals of Mathematics and Artificial Intelligence}, 1391 keywords = {belief model; belief revision; classical propositional logic; imprecise probability; order theory; possibility measure; system of spheres}, 1392 localfile = {article/DeCooman-2005-order.pdf}, 1393 number = {1}, 1394 pages = {5–34}, 1395 publisher = {Springer}, 1396 title = {Belief models: An order-theoretic investigation}, 1397 volume = {45}, 1398 year = {2005} 1399 } 1400 1401 @techreport{Williams-1975, 1402 author = {Peter M. Williams}, 1403 booktitle = {International Journal of Approximate Reasoning}, 1404 institution = {University of Sussex}, 1405 localfile = {techreport/Williams-1975.pdf}, 1406 pages = {29}, 1407 title = {Notes on conditional previsions}, 1408 volume = {44}, 1409 year = {1975} 1410 } 1411 1412 @inproceedings{DeCooman-Quaeghebeur-2009-ISIPTA, 1413 address = {Durham, United Kingdom}, 1414 author = {Gert {De Cooman} and Erik Quaeghebeur}, 1415 booktitle = {ISIPTA '09: Proceedings of the Sixth International Symposium on Imprecise Probabilities: Theories and Applications}, 1416 editor = {Thomas Augustin and Frank P. A. Coolen and Serafin Moral and Matthias C. M. Troffaes}, 1417 organization = {SIPTA}, 1418 pages = {159–168}, 1419 title = {Exchangeability for sets of desirable gambles}, 1420 year = {2009} 1421 } 1422 1423 @techreport{Nilim-ElGhaoui-2004-robust-Markov, 1424 address = {Berkeley, California}, 1425 author = {Arnab Nilim and Laurent {El Ghaoui}}, 1426 institution = {Department of Electrical Engineering and Computer Sciences}, 1427 number = {M04/26}, 1428 school = {University of California Berkeley}, 1429 title = {Robust Markov Decision Processes with Uncertain Transition Matrices}, 1430 type = {UCB ERL MEMO}, 1431 year = {2004} 1432 } 1433 1434 @misc{Doumont-2001-writing, 1435 author = {Jean-luc Doumont}, 1436 title = {Writing documents}, 1437 year = {2001} 1438 } 1439 1440 @article{Shimony-1955, 1441 author = {Abner Shimony}, 1442 issn = {0022-4812}, 1443 journal = {The Journal of Symbolic Logic}, 1444 localfile = {article/Shimony-1955.pdf}, 1445 number = {1}, 1446 pages = {1–28}, 1447 publisher = {Association for Symbolic Logic}, 1448 title = {Coherence and the Axioms of Confirmation}, 1449 url = {http://www.jstor.org/stable/2268039}, 1450 volume = {20}, 1451 year = {1955} 1452 } 1453 1454 @book{Acta-Numerica-2004, 1455 editor = {A. Iserles}, 1456 publisher = {Cambridge University Press}, 1457 title = {Acta Numerica 2004}, 1458 year = {2004} 1459 } 1460 1461 @proceedings{IPMU-1996, 1462 booktitle = {Proceedings of the Sixth International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems: IPMU 96}, 1463 title = {Proceedings of the Sixth International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems: IPMU 96}, 1464 year = {1996} 1465 } 1466 1467 @article{Troffaes-2007-decision, 1468 abstract = {Various ways for decision making with imprecise 1469 probabilities—admissibility, maximal expected utility, maximality, 1470 E-admissibility, $\Gamma$-maximax, $\Gamma$-maximin, all of which are well known 1471 from the literature—are discussed and compared. We generalise a well-known 1472 sufficient condition for existence of optimal decisions. A simple numerical 1473 example shows how these criteria can work in practice, and demonstrates their 1474 differences. Finally, we suggest an efficient approach to calculate optimal 1475 decisions under these decision criteria.}, 1476 author = {Matthias C. M. Troffaes}, 1477 doi = {10.1016/j.ijar.2006.06.001}, 1478 journal = {International Journal of Approximate Reasoning}, 1479 keywords = {Decision; E-admissibility; Lower prevision; Maximality; Maximin; Optimality; Probability; Uncertainty}, 1480 localfile = {article/Troffaes-2007-decision.pdf}, 1481 number = {1}, 1482 pages = {17–29}, 1483 title = {Decision making under uncertainty using imprecise probabilities}, 1484 volume = {45}, 1485 year = {2007} 1486 } 1487 1488 @book{Floudas-Pardalos-2009, 1489 edition = {2}, 1490 editor = {Christodoulos A. Floudas and Panos M. Pardalos}, 1491 publisher = {Springer}, 1492 series = {Springer Reference}, 1493 title = {Encyclopedia of Optimization}, 1494 year = {2009} 1495 } 1496 1497 @book{Nuutila-1995-transcl, 1498 author = {Esko Nuutila}, 1499 number = {74}, 1500 publisher = {Finnish Academy of Technology}, 1501 series = {Acta Polytechnica Scandinavica, Mathematics and Computing in Engineering Series}, 1502 title = {Efficient Transitive Closure Computation in Large Digraphs}, 1503 url = {http://www.cs.hut.fi/~enu/thesis.html}, 1504 year = {1995} 1505 } 1506 1507 @article{Connor-Mosimann-1969, 1508 annote = {ook op papier}, 1509 author = {Robert J. Connor and James E. Mosimann}, 1510 journal = {Journal of the American Statistical Association}, 1511 localfile = {article/Conner-Mosimann-1969.pdf}, 1512 number = {325}, 1513 pages = {194–206}, 1514 title = {Concepts of independence for proportions with a generalization of the Dirichlet distribution}, 1515 url = {http://www.jstor.org/stable/2283728}, 1516 volume = {64}, 1517 year = {1969} 1518 } 1519 1520 @inproceedings{Zaffalon-2001, 1521 address = {Ithaca, New York}, 1522 author = {Marco Zaffalon}, 1523 booktitle = {ISIPTA '01: Proceedings of the Second International Symposium on Imprecise Probabilities and Their Applications}, 1524 editor = {Gert {De Cooman} and Terrence L. Fine and Teddy Seidenfeld}, 1525 pages = {384–393}, 1526 publisher = {Shaker Publishing, Maastricht, The Netherlands}, 1527 title = {Statistical inference of the naive credal classifier}, 1528 year = {2001} 1529 } 1530 1531 @article{Miranda-DeCooman-Quaeghebeur-2007-Hausdorff, 1532 abstract = {We investigate to what extent finitely additive probability 1533 measures on the unit interval are determined by their moment sequence. We do 1534 this by studying the lower envelope of all finitely additive probability 1535 measures with a given moment sequence. Our investigation leads to several 1536 elegant expressions for this lower envelope, and it allows us to conclude that 1537 the information provided by the moments is equivalent to the one given by the 1538 associated lower and upper distribution functions.}, 1539 author = {Enrique Miranda and Gert {De Cooman} and Erik Quaeghebeur}, 1540 doi = {10.1007/s10959-007-0055-4}, 1541 journal = {Journal of Theoretical Probability}, 1542 keywords = {Hausdorff moment problem; coherent lower prevision; complete monotonicity; lower distribution function}, 1543 localfile = {article/Miranda-DeCooman-Quaeghebeur-2007-Hausdorff.pdf}, 1544 number = {3}, 1545 pages = {663–693}, 1546 title = {The Hausdorff Moment Problem under Finite Additivity}, 1547 volume = {20}, 1548 year = {2007} 1549 } 1550 1551 @book{Johnson-1924, 1552 address = {Cambridge, United Kingdom}, 1553 author = {W. E. Johnson}, 1554 publisher = {Cambridge University Press}, 1555 title = {Logic, Part III}, 1556 year = {1924} 1557 } 1558 1559 @article{Burge-karlin-1997, 1560 author = {Chris Burge and Samuel Karlin}, 1561 journal = {Journal of Molecular Biology}, 1562 pages = {78–94}, 1563 title = {Prediction of Complete gene Structures in Human genomic DNA}, 1564 volume = {268}, 1565 year = {1997} 1566 } 1567 1568 @book{Kemeny-Snell-Thompson-1974-finitemathintro, 1569 author = {John G. Kemeny and J. Laurie Snell and Gerald L. Thompson}, 1570 edition = {3}, 1571 publisher = {Prentice-Hall}, 1572 title = {Introduction to Finite Mathematics}, 1573 year = {1974} 1574 } 1575 1576 @article{Ovaere-Deschrijver-Kerre-2009, 1577 abstract = {In this paper we present a new approach to handle 1578 uncertainty in the Finite Element Method. As this technique is widely used to 1579 tackle real-life design problems, it is also very prone to 1580 parameter-uncertainty. It is hard to make a good decision regarding design 1581 optimization if no claim can be made with respect to the outcome of the 1582 simulation. We propose an approach that combines several techniques in order to 1583 offer a total order on the possible design choices, taking the inherent 1584 fuzziness into account. Additionally we propose a more efficient ordering 1585 procedure to build a total order on fuzzy numbers.}, 1586 annote = {ook op papier}, 1587 author = {Koen Ovaere and Glad Deschrijver and Etienne E. Kerre}, 1588 doi = {10.1007/s12543-009-0002-4}, 1589 journal = {Fuzzy Information and Engineering}, 1590 keywords = {fuzzy decision making; fuzzy finite element method; fuzzy ordering}, 1591 localfile = {article/Ovaere-deschrijver-Kerre-2009.pdf}, 1592 number = {1}, 1593 pages = {27–36}, 1594 publisher = {Springer}, 1595 title = {Application of fuzzy decision making to the fuzzy finite element method}, 1596 volume = {1}, 1597 year = {2009} 1598 } 1599 1600 @book{Brokken-2006, 1601 author = {Frank B. Brokken}, 1602 month = sep, 1603 publisher = {University of Groningen}, 1604 title = {C++ Annotations}, 1605 year = {2006} 1606 } 1607 1608 @book{BarndorffNielsen-1978, 1609 annote = {Geselecteerde delen kopies}, 1610 author = {Ole Barndorff-Nielsen}, 1611 publisher = {Wiley}, 1612 title = {Information and Exponential Families In Statistical Theory}, 1613 year = {1978} 1614 } 1615 1616 @article{Harsanyi-1982-comment, 1617 annote = {ook op papier}, 1618 author = {John C. Harsanyi}, 1619 journal = {Management Science}, 1620 localfile = {article/Harsanyi-1982-comment.pdf}, 1621 number = {2}, 1622 pages = {120–124}, 1623 title = {Subjective probability and the theory of games: Comments on Kadane and Larkey's paper}, 1624 url = {http://www.jstor.org/stable/2631295}, 1625 volume = {28}, 1626 year = {1982} 1627 } 1628 1629 @proceedings{IPMU-2004, 1630 booktitle = {Proceedings of the Tenth International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems: IPMU 2004}, 1631 title = {Proceedings of the Tenth International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems: IPMU 2004}, 1632 year = {2004} 1633 } 1634 1635 @article{Wagner-2007-Smith-Walley, 1636 annote = {op papier in Wagnerbundel}, 1637 author = {Carl G. Wagner}, 1638 doi = {10.1007/s11225-007-9064-7}, 1639 journal = {Studia Logica}, 1640 localfile = {article/Wagner-2007-Smith-Walley.pdf}, 1641 pages = {343–350}, 1642 title = {The Smith-Walley Interpretation of Subjective Probability: An Appreciation}, 1643 volume = {86}, 1644 year = {2007} 1645 } 1646 1647 @book{Davey-Priestley-1990, 1648 author = {B. A. Davey and H. A. Priestley}, 1649 publisher = {Cambridge University Press}, 1650 series = {Cambridge Mathematical Textbooks}, 1651 title = {Introduction to Lattices and Order}, 1652 year = {1990} 1653 } 1654 1655 @inproceedings{John-Langley-1995, 1656 author = {George H. John and Pat Langley}, 1657 booktitle = {Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (UAI-95)}, 1658 editor = {Philippe Besnard and Steve Hanks}, 1659 pages = {338–345}, 1660 publisher = {Morgan Kaufmann}, 1661 title = {Estimating Continuous Distributions in Bayesian Classifiers}, 1662 year = {1995} 1663 } 1664 1665 @article{Tanaka-Okuda-Asai-1973, 1666 abstract = {In problems of system analysis, it is customary to treat 1667 imprecision by the use of probability theory. It is becoming increasingly clear, 1668 however, that in the case of many real world problems involving large scale 1669 systems such as economic systems, social systems, mass service systems, etc., 1670 the major source of imprecision should more properly be labeled 'fuzziness' 1671 rather than 'randomness.' By fuzziness, we mean the type of imprecision which is 1672 associated with the lack of sharp transition from membership to nonmembership, 1673 as in tall men, small numbers, likely events, etc. In this paper our main 1674 concern is with the application of the theory of fuzzy sets to decision problems 1675 involving fuzzy goals and strategies, etc., as defined by R. E. Bellman and L. 1676 A. Zadeh [1]. However, in our approach, the emphasis is on mathematical 1677 programming and the use of the concept of a level set to extend some of the 1678 classical results to problems involving fuzzy constraints and objective 1679 functions.}, 1680 author = {Hideo Tanaka and Tetsuji Okuda and Kiyoji Asai}, 1681 doi = {10.1080/01969727308545912}, 1682 journal = {Cybernetics and Systems: An International Journal}, 1683 number = {4}, 1684 pages = {37–46}, 1685 title = {On Fuzzy-Mathematical Programming}, 1686 volume = {3}, 1687 year = {1973} 1688 } 1689 1690 @article{Diaconis-Ylvisaker-1979, 1691 abstract = {Let X be a random vector distributed according to an 1692 exponential family with natural parameter $\theta$ ∈ $\Theta$. We characterize 1693 conjugate prior measures on $\Theta$ through the property of linear posterior 1694 expectation of the mean parameter of X : E{E(X|$\theta$)|X = x} = ax + b. We 1695 also delineate which hyperparameters permit such conjugate priors to be 1696 proper.}, 1697 annote = {geannoteerde kopie}, 1698 author = {Persi Diaconis and Donald Ylvisaker}, 1699 doi = {10.1214/aos}, 1700 journal = {The Annals of Statistics}, 1701 keywords = {Bayes; conjugate priors; linearity of regression}, 1702 localfile = {article/Diaconis-Ylvisaker-1979.pdf}, 1703 number = {2}, 1704 pages = {269–281}, 1705 publisher = {Institute of Mathematical Statistics}, 1706 title = {Conjugate priors for exponential families}, 1707 volume = {7}, 1708 year = {1979} 1709 } 1710 1711 @proceedings{ISIPTA-2001, 1712 address = {Ithaca, New York}, 1713 booktitle = {ISIPTA '01: Proceedings of the Second International Symposium on Imprecise Probabilities and Their Applications}, 1714 editor = {Gert {De Cooman} and Terrence L. Fine and Teddy Seidenfeld}, 1715 publisher = {Shaker Publishing, Maastricht, The Netherlands}, 1716 title = {ISIPTA '01: Proceedings of the Second International Symposium on Imprecise Probabilities and Their Applications}, 1717 year = {2001} 1718 } 1719 1720 @article{Miranda-Combarro-Gil-2006-extreme, 1721 abstract = {Non-additive measures are a valuable tool to model many 1722 different problems arising in real situations. However, two important 1723 difficulties appear in their practical use: the complexity of the measures and 1724 their identification from sample data. For the first problem, additional 1725 conditions are imposed, leading to different subfamilies of non-additive 1726 measures. Related to the second point, in this paper we study the set of 1727 vertices of some families of non-additive measures, namely k-additive measures 1728 and p-symmetric measures. These extreme points are necessary in order to 1729 properly apply a new method of identification of non-additive measures based on 1730 genetic algorithms, whose cross-over operator is the convex combination. We 1731 solve the problem through techniques of Linear Programming.}, 1732 author = {Pedro Miranda and Elías F. Combarro and Pedro Gil}, 1733 doi = {10.1016/j.ejor.2005.03.005}, 1734 journal = {European Journal of Operational Research}, 1735 keywords = {Decision analysis; Genetic algorithms; Linear programming; Multiple criteria analysis; Non-additive measures; Vertices; k-additivity; p-symmetry}, 1736 localfile = {article/Miranda-Combarro-Gil-2006-extreme.pdf}, 1737 number = {3}, 1738 pages = {1865–1884}, 1739 title = {Extreme points of some families of non-additive measures}, 1740 volume = {174}, 1741 year = {2006} 1742 } 1743 1744 @article{Miranda-DeCooman-Couso-2005-multivalued, 1745 abstract = {We discuss how lower previsions induced by multi-valued 1746 mappings fit into the framework of the behavioural theory of imprecise 1747 probabilities, and show how the notions of coherence and natural extension from 1748 that theory can be used to prove and generalise existing results in an elegant 1749 and straightforward manner. This provides a clear example for their explanatory 1750 and unifying power.}, 1751 annote = {uitgebreide versie, ook op papier}, 1752 author = {Enrique Miranda and Gert {De Cooman} and Inés Couso}, 1753 doi = {10.1016/j.jspi.2004.03.005}, 1754 journal = {Journal of Statistical Planning and Inference}, 1755 keywords = {Coherence; Conditioning; Evidence theory; Imprecise probabilities; Lower inverse; Lower prevision; Multi-valued mapping; Natural extension; Random set}, 1756 localfile = {article/Miranda-DeCooman-Couso-2005-multivalued.pdf}, 1757 number = {1}, 1758 pages = {173–197}, 1759 title = {Lower previsions induced by multi-valued mappings}, 1760 volume = {133}, 1761 year = {2005} 1762 } 1763 1764 @article{Wagner-2003-uniformity-rule, 1765 annote = {op papier in Wagnerbundel}, 1766 author = {Carl G. Wagner}, 1767 journal = {Erkenntnis}, 1768 pages = {349–364}, 1769 title = {Commuting probability revisions: the uniformity rule}, 1770 volume = {59}, 1771 year = {2003} 1772 } 1773 1774 @article{Bruening-Dennenberg-2008-belELP, 1775 abstract = {It is known that the $\sigma$-additive Möbius transform of a 1776 belief function (we prefer to call it belief measure) can be derived from 1777 Choquet's Theorem. One has to show that the extreme points of the compact convex 1778 set of belief measures are the {0,1}-valued belief measures, which are called 1779 filter games as well. A proof is implicit in the famous 1953/54 paper of Choquet 1780 but it is hard to read it. We present a direct proof and – for the sake of 1781 completeness – derive the Möbius transform.}, 1782 annote = {explicitation of an implicit result of Choquet-1954}, 1783 author = {Martin Brüning and Dieter Denneberg}, 1784 doi = {10.1016/j.ijar.2006.11.003}, 1785 journal = {International Journal of Approximate Reasoning}, 1786 localfile = {article/Bruening-Dennenberg-2007-belELP.pdf}, 1787 number = {3}, 1788 pages = {670–675}, 1789 publisher = {Elsevier}, 1790 title = {The extreme points of the set of belief measures}, 1791 volume = {48}, 1792 year = {2008} 1793 } 1794 1795 @article{Epstein-Seo-2010, 1796 abstract = {The de Finetti Theorem is a cornerstone of the Bayesian 1797 approach. Bernardo (1996, p. 5) writes that its “message is very clear: if a 1798 sequence of observations is judged to be exchangeable, then any subset of them 1799 must be regarded as a random sample from some model, and there exists a prior 1800 distribution on the parameter of such model, hence requiring a Bayesian 1801 approach.” We argue that although exchangeability, interpreted as symmetry of 1802 evidence, is a weak assumption, when combined with subjective expected utility 1803 theory, it also implies complete confidence that experiments are identical. When 1804 evidence is sparse and there is little evidence of symmetry, this implication of 1805 de Finetti's hypotheses is not intuitive. This motivates our adoption of 1806 multiple-priors utility as the benchmark model of preference. We provide two 1807 alternative generalizations of the de Finetti Theorem for this framework. A 1808 model of updating is also provided.}, 1809 author = {Larry G. Epstein and Kyoungwon Seo}, 1810 doi = {10.3982/TE596}, 1811 issn = {1555-7561}, 1812 journal = {Theoretical Economics}, 1813 keywords = {ambiguity; exchangeability; learning; multiple priors; symmetry; updating}, 1814 localfile = {article/Epstein-Seo-2010.pdf}, 1815 number = {3}, 1816 pages = {313–368}, 1817 publisher = {Blackwell Publishing Ltd}, 1818 title = {Symmetry of evidence without evidence of symmetry}, 1819 volume = {5}, 1820 year = {2010} 1821 } 1822 1823 @article{Rho-Tang-Ye-2010, 1824 abstract = {The advances of next-generation sequencing technology have 1825 facilitated metagenomics research that attempts to determine directly the whole 1826 collection of genetic material within an environmental sample (i.e. the 1827 metagenome). Identification of genes directly from short reads has become an 1828 important yet challenging problem in annotating metagenomes, since the assembly 1829 of metagenomes is often not available. Gene predictors developed for whole 1830 genomes (e.g. Glimmer) and recently developed for metagenomic sequences (e.g. 1831 MetaGene) show a significant decrease in performance as the sequencing error 1832 rates increase, or as reads get shorter. We have developed a novel gene 1833 prediction method FragGeneScan, which combines sequencing error models and codon 1834 usages in a hidden Markov model to improve the prediction of protein-coding 1835 region in short reads. The performance of FragGeneScan was comparable to Glimmer 1836 and MetaGene for complete genomes. But for short reads, FragGeneScan 1837 consistently outperformed MetaGene (accuracy improved ~62\% for reads of 400 1838 bases with 1\% sequencing errors, and ~18\% for short reads of 100 bases that 1839 are error free). When applied to metagenomes, FragGeneScan recovered 1840 substantially more genes than MetaGene predicted (>90\% of the genes identified 1841 by homology search), and many novel genes with no homologs in current protein 1842 sequence database.}, 1843 author = {Mina Rho and Haixu Tang and Yuzhen Ye}, 1844 doi = {10.1093/nar}, 1845 journal = {Nucleic Acids Research}, 1846 localfile = {article/Rho-Tang-Ye-2010.pdf}, 1847 number = {20}, 1848 pages = {e191}, 1849 title = {FragGeneScan: predicting genes in short and error-prone reads}, 1850 volume = {38}, 1851 year = {2010} 1852 } 1853 1854 @article{Utkin-Augustin-2007, 1855 abstract = {The paper presents an efficient solution to decision 1856 problems where direct partial information on the distribution of the states of 1857 nature is available, either by observations of previous repetitions of the 1858 decision problem or by direct expert judgements. To process this information we 1859 use a recent generalization of Walley's imprecise Dirichlet model, allowing us 1860 also to handle incomplete observations or imprecise judgements, including 1861 missing data. We derive efficient algorithms and discuss properties of the 1862 optimal solutions with respect to several criteria, including Gamma-maximinity 1863 and E-admissibility. In the case of precise data and pure actions the former 1864 surprisingly leads us to a frequency-based variant of the Hodges–Lehmann 1865 criterion, which was developed in classical decision theory as a compromise 1866 between Bayesian and minimax procedures.}, 1867 author = {Lev V. Utkin and Thomas Augustin}, 1868 journal = {International Journal of Approximate Reasoning}, 1869 keywords = {Belief functions; Coarse data; Decision making; E-admissibility; Imprecise Dirichlet model (IDM); Imprecise probabilities; Incomplete data; Interval probability; Interval statistical models; Missing or set-valued statistical data}, 1870 localfile = {article/Utkin-Augustin-2007.pdf}, 1871 number = {3}, 1872 pages = {322–338}, 1873 title = {Decision making under incomplete data using the imprecise Dirichlet model}, 1874 volume = {44}, 1875 year = {2007} 1876 } 1877 1878 @inproceedings{DeCooman-Troffaes-Miranda-2005, 1879 address = {Pittsburgh, Pennsylvania}, 1880 author = {Gert {De Cooman} and Matthias C. M. Troffaes and Enrique Miranda}, 1881 booktitle = {ISIPTA '05: Proceedings of the Fourth International Symposium on Imprecise Probabilities and Their Applications}, 1882 editor = {Fabio Gagliardi Cozman and Robert Nau and Teddy Seidenfeld}, 1883 organization = {SIPTA}, 1884 pages = {145–154}, 1885 title = {n-Monotone lower previsions and lower integrals}, 1886 year = {2005} 1887 } 1888 1889 @inproceedings{Fortet-1951, 1890 address = {Paris}, 1891 author = {Robert M. Fortet}, 1892 booktitle = {Congrès international de philosophie des sciences. 4: Calcul des probabilités}, 1893 editor = {Raymond Bayer}, 1894 number = {1146}, 1895 pages = {35–47}, 1896 publisher = {Hermann}, 1897 series = {Actualités scientifiques et industrielles}, 1898 title = {Faut-il élargir les axiomes du calcul des probabilités?}, 1899 year = {1951} 1900 } 1901 1902 @inproceedings{Wilson-Moral-1994, 1903 author = {Nic Wilson and Serafín Moral}, 1904 booktitle = {ECAI 94: Proceedings of the 11th European Conference on Artificial Intelligence}, 1905 editor = {A. Cohn}, 1906 pages = {386–390}, 1907 publisher = {John Wiley \& Sons}, 1908 title = {A logical view of probability}, 1909 year = {1994} 1910 } 1911 1912 @article{Munch-etal-2006, 1913 abstract = {BACKGROUND: Genomic tiling micro arrays have great potential 1914 for identifying previously undiscovered coding as well as non-coding 1915 transcription. To-date, however, analyses of these data have been performed in 1916 an ad hoc fashion. RESULTS: We present a probabilistic procedure, ExpressHMM, 1917 that adaptively models tiling data prior to predicting expression on genomic 1918 sequence. A hidden Markov model (HMM) is used to model the distributions of 1919 tiling array probe scores in expressed and non-expressed regions. The HMM is 1920 trained on sets of probes mapped to regions of annotated expression and 1921 non-expression. Subsequently, prediction of transcribed fragments is made on 1922 tiled genomic sequence. The prediction is accompanied by an expression 1923 probability curve for visual inspection of the supporting evidence. We test 1924 ExpressHMM on data from the Cheng et al. (2005) tiling array experiments on ten 1925 Human chromosomes [1]. Results can be downloaded and viewed from our web site 1926 [2]. CONCLUSION: The value of adaptive modelling of fluorescence scores prior to 1927 categorisation into expressed and non-expressed probes is demonstrated. Our 1928 results indicate that our adaptive approach is superior to the previous analysis 1929 in terms of nucleotide sensitivity and transfrag specificity.}, 1930 author = {Kasper Munch and Paul Gardner and Peter Arctander and Anders Krogh}, 1931 doi = {10.1186/1471-2105-7-239}, 1932 issn = {1471-2105}, 1933 journal = {BMC Bioinformatics}, 1934 localfile = {article/Munch-etal-2006.pdf}, 1935 number = {1}, 1936 pages = {239}, 1937 publisher = {BioMed Central Ltd}, 1938 title = {A hidden Markov model approach for determining expression from genomic tiling micro arrays}, 1939 volume = {7}, 1940 year = {2006} 1941 } 1942 1943 @phdthesis{Mevel-1997, 1944 author = {Laurent Mevel}, 1945 school = {Université de Rennes}, 1946 title = {Statistique asymptotique pour les modèles de Markov cachés}, 1947 year = {1997} 1948 } 1949 1950 @article{DeCooman-2001, 1951 abstract = {The paper discusses integration and some aspects of 1952 conditioning in numerical possibility theory, where possibility measures have 1953 the behavioural interpretation of upper probabilities, that is, systems of upper 1954 betting rates. In such a context, integration can be used to extend upper 1955 probabilities to upper previsions. It is argued that the role of the fuzzy 1956 integral in this context is limited, as it can only be used to define a coherent 1957 upper prevision if the associated upper probability is 0–1-valued, in which 1958 case it moreover coincides with the Choquet integral. These results are valid 1959 for arbitrary coherent upper probabilities, and therefore also relevant for 1960 possibility theory. It follows from the discussion that in a numerical context, 1961 the Choquet integral is better suited than the fuzzy integral for producing 1962 coherent upper previsions starting from possibility measures. At the same time, 1963 alternative expressions for the Choquet integral associated with a possibility 1964 measure are derived. Finally, it is shown that a possibility measure is fully 1965 conglomerable and satisfies Walley's regularity axiom for conditioning, ensuring 1966 that it can be coherently extended to a conditional possibility measure using 1967 both the methods of natural and regular extension.}, 1968 author = {Gert {De Cooman}}, 1969 doi = {10.1023/A:1016705331195}, 1970 journal = {Annals of Mathematics and Artificial Intelligence}, 1971 localfile = {article/DeCooman-2001.pdf}, 1972 month = aug, 1973 number = {1}, 1974 pages = {87–123}, 1975 publisher = {Springer}, 1976 title = {Integration and conditioning in numerical possibility theory}, 1977 volume = {32}, 1978 year = {2001} 1979 } 1980 1981 @book{Johnson-Kotz-Balakrishnan-1997, 1982 author = {Norman L. Johnson and Samuel Kotz and N. Balakrishnan}, 1983 publisher = {Wiley}, 1984 series = {Wiley Series in Probability and Statistics}, 1985 title = {Discrete Multivariate Distributions}, 1986 year = {1997} 1987 } 1988 1989 @article{Casalis-1996, 1990 abstract = {The present paper describes all the natural exponential 1991 families on \mathbb{R}^d whose variance function is of the form V(m) = am øtimes 1992 m + B(m) + C, with m øtimes m($\theta$) = \langle $\theta$, m \rangle m and B 1993 linear in m. There are 2d + 4 types of such families, which are built from 1994 particular mixtures of families of Normal, Poisson, gamma, hyperbolic on 1995 \mathbb{R}^d and negative-multinomial distributions. The proof of this result 1996 relies mainly on techniques used in the elementary theory of Lie algebras.}, 1997 author = {M. Casalis}, 1998 doi = {10.1214/aos}, 1999 issn = {0090-5364}, 2000 journal = {The Annals of Statistics}, 2001 keywords = {Morris class; Variance functions}, 2002 localfile = {article/Casalis-1996.pdf}, 2003 number = {4}, 2004 pages = {1828–1854}, 2005 publisher = {Institute of Mathematical Statistics}, 2006 title = {The 2d+4 simple quadratic natural exponential families on R^d}, 2007 url = {http://www.jstor.org/stable/2242752}, 2008 volume = {24}, 2009 year = {1996} 2010 } 2011 2012 @article{DeCooman-etal-2010, 2013 abstract = {We focus on credal nets, which are graphical models that 2014 generalise Bayesian nets to imprecise probability. We replace the notion of 2015 strong independence commonly used in credal nets with the weaker notion of 2016 epistemic irrelevance, which is arguably more suited for a behavioural theory of 2017 probability. Focusing on directed trees, we show how to combine the given local 2018 uncertainty models in the nodes of the graph into a global model, and we use 2019 this to construct and justify an exact message-passing algorithm that computes 2020 updated beliefs for a variable in the tree. The algorithm, which is linear in 2021 the number of nodes, is formulated entirely in terms of coherent lower 2022 previsions, and is shown to satisfy a number of rationality requirements. We 2023 supply examples of the algorithm's operation, and report an application to 2024 on-line character recognition that illustrates the advantages of our approach 2025 for prediction. We comment on the perspectives, opened by the availability, for 2026 the first time, of a truly efficient algorithm based on epistemic irrelevance.}, 2027 author = {Gert {De Cooman} and Filip Hermans and Alessandro Antonucci and Marco Zaffalon}, 2028 doi = {10.1016/j.ijar.2010.08.011}, 2029 issn = {0888-613X}, 2030 journal = {International Journal of Approximate Reasoning}, 2031 keywords = {Coherence; Credal net; Epistemic irrelevance; Hidden Markov model; Separation; Strong independence}, 2032 localfile = {article/DeCooman-etal-2010.pdf}, 2033 number = {9}, 2034 pages = {1029–1052}, 2035 publisher = {Elsevier}, 2036 title = {Epistemic irrelevance in credal nets: the case of imprecise Markov trees}, 2037 volume = {51}, 2038 year = {2010} 2039 } 2040 2041 @inproceedings{Quaeghebeur-DeCooman-2003-PhDsymp, 2042 address = {Ghent, Belgium}, 2043 author = {Erik Quaeghebeur and Gert {De Cooman}}, 2044 booktitle = {Proceedings of the Fourth UGent-FTW PhD Symposium}, 2045 title = {Command line completion: an illustration of learning and decision making using the imprecise Dirichlet model}, 2046 year = {2003} 2047 } 2048 2049 @article{Kadane-Larkey-1982, 2050 annote = {ook op papier}, 2051 author = {Joseph B. Kadane and Patrick D. Larkey}, 2052 journal = {Management Science}, 2053 localfile = {article/Kadane-Larkey-1982.pdf}, 2054 number = {2}, 2055 pages = {113–120}, 2056 title = {Subjective probability and the theory of games}, 2057 url = {http://www.jstor.org/stable/2631294}, 2058 volume = {28}, 2059 year = {1982} 2060 } 2061 2062 @book{Fudenberg-Levine-1998, 2063 annote = {geannoteerde uittreksels}, 2064 author = {Drew Fudenberg and David K. Levine}, 2065 editor = {Ken Binmore}, 2066 number = {2}, 2067 publisher = {The MIT Press}, 2068 series = {MIT Press Series on Economic Learning and Social Evolution}, 2069 title = {The Theory of Learning in Games}, 2070 year = {1998} 2071 } 2072 2073 @article{Bellman-Zadeh-1970, 2074 abstract = {By decision-making in a fuzzy environment is meant a 2075 decision process in which the goals and/or the constraints, but not necessarily 2076 the system under control, are fuzzy in nature. This means that the goals and/or 2077 the constraints constitute classes of alternatives whose boundaries are not 2078 sharply defined. An example of a fuzzy constraint is: "The cost of A should not 2079 be substantially higher than $\alpha$," where $\alpha$ is a specified constant. 2080 Similarly, an example of a fuzzy goal is: "$\chi$ should be in the vicinity of 2081 $\chi$0," where $\chi$0 is a constant. The italicized words are the sources of 2082 fuzziness in these examples. Fuzzy goals and fuzzy constraints can be defined 2083 precisely as fuzzy sets in the space of alternatives. A fuzzy decision, then, 2084 may be viewed as an intersection of the given goals and constraints. A 2085 maximizing decision is defined as a point in the space of alternatives at which 2086 the membership function of a fuzzy decision attains its maximum value. The use 2087 of these conc}, 2088 author = {R. E. Bellman and L. A. Zadeh}, 2089 doi = {10.1287/mnsc.17.4.B141}, 2090 issn = {0025-1909}, 2091 journal = {Management Science}, 2092 localfile = {article/Bellman-Zadeh-1970.pdf}, 2093 number = {4}, 2094 pages = {141–164}, 2095 publisher = {INFORMS}, 2096 title = {Decision-making in a fuzzy environment}, 2097 volume = {17}, 2098 year = {1970} 2099 } 2100 2101 @article{Zaffalon-2002-missing, 2102 abstract = {This paper proposes an exact, no-assumptions approach to 2103 dealing with incomplete sets of multivariate categorical data. An incomplete 2104 data set is regarded as a 1nite collection of complete data sets, and a joint 2105 distribution is obtained from each of them, at a descriptive level. The tools to 2106 simultaneously treat all the possible joint distributions compatible with an 2107 incomplete set of data are given. In particular, a linear description of the set 2108 of distributions is formulated, and it is shown that the computation of bounds 2109 on the expectation of real-valued functions under such distributions is both 2110 possible and efficient, by means of linear programming. Specific algorithms are 2111 also developed whose complexity grows linearly in the number of observations. An 2112 analysis is then carried out to estimate population probabilities from 2113 incomplete multinomial samples. The descriptive tool extends in a 2114 straightforward way to the inferential problem by exploiting Walley s imprecise 2115 Dirichlet model.}, 2116 author = {Marco Zaffalon}, 2117 doi = {10.1016/S0378-3758(01)00206-3}, 2118 journal = {Journal of Statistical Planning and Inference}, 2119 keywords = {Belief functions; Credal sets; Flow network; Imprecise Dirichlet model; Imprecise probabilities; Incomplete data; Linear optimization}, 2120 localfile = {article/Zaffalon-2002-missing.pdf}, 2121 pages = {105–122}, 2122 title = {Exact credal treatment of missing data}, 2123 url = {http://www.sciencedirect.com/science/article/pii/S0378375801002063}, 2124 volume = {105}, 2125 year = {2002} 2126 } 2127 2128 @inproceedings{Strens-2000, 2129 author = {Malcolm Strens}, 2130 booktitle = {Proceedings of the 17th International Conference on Machine Learning (ICML-2000)}, 2131 title = {A Bayesian Framework for Reinforcement Learning}, 2132 year = {2000} 2133 } 2134 2135 @phdthesis{Coolen-1994, 2136 author = {Frank P. A. Coolen}, 2137 school = {Technische Universiteit Eindhoven}, 2138 title = {Statistical Modelling of Expert Opinions Using Imprecise Probabilities}, 2139 year = {1994} 2140 } 2141 2142 @article{DeCooman-Zaffalon-2004-incomplete, 2143 abstract = {Currently, there is renewed interest in the problem, raised 2144 by Shafer in 1985, of updating probabilities when observations are incomplete 2145 (or set-valued). This is a fundamental problem in general, and of particular 2146 interest for Bayesian networks. Recently, Grünwald and Halpern have shown that 2147 commonly used updating strategies fail in this case, except under very special 2148 assumptions. In this paper we propose a new method for updating probabilities 2149 with incomplete observations. Our approach is deliberately conservative: we make 2150 no assumptions about the so-called incompleteness mechanism that associates 2151 complete with incomplete observations. We model our ignorance about this 2152 mechanism by a vacuous lower prevision, a tool from the theory of imprecise 2153 probabilities, and we use only coherence arguments to turn prior into posterior 2154 (updated) probabilities. In general, this new approach to updating produces 2155 lower and upper posterior probabilities and previsions (expectations), as well 2156 as partially determinate decisions. This is a logical consequence of the 2157 existing ignorance about the incompleteness mechanism. As an example, we use the 2158 new updating method to properly address the apparent paradox in the [`]Monty 2159 Hall' puzzle. More importantly, we apply it to the problem of classification of 2160 new evidence in probabilistic expert systems, where it leads to a new, so-called 2161 conservative updating rule. In the special case of Bayesian networks constructed 2162 using expert knowledge, we provide an exact algorithm to compare classes based 2163 on our updating rule, which has linear-time complexity for a class of networks 2164 wider than polytrees. This result is then extended to the more general framework 2165 of credal networks, where computations are often much harder than with Bayesian 2166 nets. Using an example, we show that our rule appears to provide a solid basis 2167 for reliable updating with incomplete observations, when no strong assumptions 2168 about the incompleteness mechanism are justified.}, 2169 author = {Gert {De Cooman} and Marco Zaffalon}, 2170 doi = {10.1016/j.artint.2004.05.006}, 2171 issn = {0004-3702}, 2172 journal = {Artificial Intelligence}, 2173 keywords = {Incomplete observations; Updating probabilities}, 2174 localfile = {article/DeCooman-Zaffalon-2004-incomplete.pdf}, 2175 number = {1-2}, 2176 pages = {75–125}, 2177 publisher = {Elsevier}, 2178 title = {Updating beliefs with incomplete observations}, 2179 volume = {159}, 2180 year = {2004} 2181 } 2182 2183 @article{Liu-Mueller-2003, 2184 author = {Xueli Liu and Hans-Georg Müller}, 2185 doi = {10.1093/bioinformatics}, 2186 journal = {Bioinformatics}, 2187 localfile = {article/Liu-Mueller-2003.pdf}, 2188 number = {15}, 2189 pages = {1937–1944}, 2190 title = {Modes and clustering for time-warped gene expression profile data}, 2191 volume = {19}, 2192 year = {2003} 2193 } 2194 2195 @book{DeGroot-2004, 2196 annote = {Wiley Classics Library Edition}, 2197 author = {Morris H. DeGroot}, 2198 publisher = {Wiley}, 2199 title = {Optimal Statistical Decisions}, 2200 year = {2004} 2201 } 2202 2203 @article{Benaim-Hirsch-1999, 2204 abstract = {Fictitious play in infinitely repeated, randomly perturbed 2205 games is investigated. Dynamical systems theory is used to study the Markov 2206 process {x\_k}, whose state vector x\_k lists the empirical frequencies of 2207 player's actions in the first k games. For 2 × 2 games with countably many Nash 2208 distribution equilibria, we prove that sample paths converge almost surely. But 2209 for Jordan's 3 × 2 matching game, there are robust parameter values giving 2210 probability 0 of convergence. Applications are made to coordination and 2211 anticoordination games and to general theory. Proofs rely on results in 2212 stochastic approximation and dynamical systems.}, 2213 annote = {op papier}, 2214 author = {Michael Benaïm and Morris W. Hirsch}, 2215 doi = {10.1006/game.1999.0717}, 2216 issn = {0899-8256}, 2217 journal = {Games and Economic Behavior}, 2218 month = oct, 2219 number = {1-2}, 2220 pages = {36–72}, 2221 title = {Mixed Equilibria and Dynamical Systems Arising from Fictitious Play in Perturbed Games}, 2222 volume = {29}, 2223 year = {1999} 2224 } 2225 2226 @incollection{Brams-Fishburn-1991-altvote, 2227 author = {Steven J. Brams and Peter C. Fishburn}, 2228 booktitle = {Political Pareties and Elections in the United States: An Encyclopedia}, 2229 editor = {Sandy L Maisel}, 2230 pages = {23–31}, 2231 publisher = {garland}, 2232 title = {Alternative voting systems}, 2233 url = {http://bcn.boulder.co.us/government/approvalvote/altvote.html}, 2234 volume = {1}, 2235 year = {1991} 2236 } 2237 2238 @incollection{Miranda-DeCooman-Quaeghebeur-2008-IPMU2006, 2239 author = {Enrique Miranda and Gert {De Cooman} and Erik Quaeghebeur}, 2240 booktitle = {Uncertainty and Intelligent Information Systems}, 2241 chapter = {3}, 2242 editor = {Bernadette Bouchon-Meunier and R. R. Yager and C. Marsala and M. Rifqi}, 2243 pages = {33–45}, 2244 publisher = {World Scientific}, 2245 title = {The moment problem for finitely additive probabilities}, 2246 url = {http://www.worldscibooks.com/compsci/6747.html}, 2247 year = {2008} 2248 } 2249 2250 @article{Dubois-Prade-Sabbadin-2001, 2251 author = {Didier Dubois and Henri Prade and Régis Sabbadin}, 2252 doi = {10.1016/S0377-2217(99)00473-7}, 2253 journal = {European Journal of Operational Research}, 2254 keywords = {decision theory; possibility theory; uncertainty}, 2255 localfile = {article/Dubois-Prade-Sabbadin-2001.pdf}, 2256 pages = {459–478}, 2257 title = {Decision-theoretic foundations of qualitative possibility theory}, 2258 volume = {128}, 2259 year = {2001} 2260 } 2261 2262 @techreport{Hofbauer-1995, 2263 author = {Josef Hofbauer}, 2264 institution = {Collegium Budapest}, 2265 title = {Stability for the Best Response Dynamics}, 2266 year = {1995} 2267 } 2268 2269 @article{Derriennic-1985, 2270 author = {Marie-Madeleine Derriennic}, 2271 journal = {Journal of Approximation Theory}, 2272 pages = {155–166}, 2273 title = {On Multivariate Approximation by Bernstein-Type Polynomials}, 2274 volume = {45}, 2275 year = {1985} 2276 } 2277 2278 @article{Amara-1995-wavelets, 2279 annote = {op papier}, 2280 author = {Amara Graps}, 2281 journal = {IEEE Computational Science and Engineering}, 2282 number = {2}, 2283 publisher = {IEEE Computer Society}, 2284 title = {An Introduction to Wavelets}, 2285 volume = {2}, 2286 year = {1995} 2287 } 2288 2289 @inproceedings{Bouckaert-2004, 2290 author = {Remco R. Bouckaert}, 2291 booktitle = {AI 2004: Advances in Artificial Intelligence: 17th Australian Joint Conference on Artificial Intelligence}, 2292 editor = {Geoffrey I. Webb and Xinghuo Yu}, 2293 pages = {1089–1094}, 2294 publisher = {Springer}, 2295 series = {Lecture Notes in AI}, 2296 title = {Naive Bayes Classifiers that Perform Well with Continuous Variables}, 2297 year = {2004} 2298 } 2299 2300 @article{Gillett-et-al-2007, 2301 abstract = {This article presents a probabilistic logic whose sentences 2302 can be interpreted as asserting the acceptability of gambles described in terms 2303 of an underlying logic. This probabilistic logic has a concrete syntax and a 2304 complete inference procedure, and it handles conditional as well as 2305 unconditional probabilities. It synthesizes Nilsson's probabilistic logic and 2306 Frisch and Haddawy's anytime inference procedure with Wilson and Moral's logic 2307 of gambles. Two distinct semantics can be used for our probabilistic logic: (1) 2308 the measure-theoretic semantics used by the prior logics already mentioned and 2309 also by the more expressive logic of Fagin, Halpern, and Meggido and (2) a 2310 behavioral semantics. Under the measure-theoretic semantics, sentences of our 2311 probabilistic logic are interpreted as assertions about a probability 2312 distribution over interpretations of the underlying logic. Under the behavioral 2313 semantics, these sentences are interpreted only as asserting the acceptability 2314 of gambles, and this suggests different directions for generalization.}, 2315 annote = {Reasoning with Imprecise Probabilities}, 2316 author = {Peter R. Gillett and Richard B. Scherl and Glenn Shafer}, 2317 doi = {10.1016/j.ijar.2006.07.014}, 2318 issn = {0888-613X}, 2319 journal = {International Journal of Approximate Reasoning}, 2320 keywords = {Anytime deduction; Behavioral semantics; Gambles; Measure–theoretic; Probabilistic logic}, 2321 localfile = {article/Gillett-et-al-2007.pdf}, 2322 number = {3}, 2323 pages = {281–300}, 2324 title = {A probabilistic logic based on the acceptability of gambles}, 2325 volume = {44}, 2326 year = {2007} 2327 } 2328 2329 @article{Zhu-Lomsadze-Borodovsky-2010, 2330 abstract = {We describe an algorithm for gene identification in DNA 2331 sequences derived from shotgun sequencing of microbial communities. Accurate ab 2332 initio gene prediction in a short nucleotide sequence of anonymous origin is 2333 hampered by uncertainty in model parameters. While several machine learning 2334 approaches could be proposed to bypass this difficulty, one effective method is 2335 to estimate parameters from dependencies, formed in evolution, between 2336 frequencies of oligonucleotides in protein-coding regions and genome nucleotide 2337 composition. Original version of the method was proposed in 1999 and has been 2338 used since for (i) reconstructing codon frequency vector needed for gene finding 2339 in viral genomes and (ii) initializing parameters of self-training gene finding 2340 algorithms. With advent of new prokaryotic genomes en masse it became possible 2341 to enhance the original approach by using direct polynomial and logistic 2342 approximations of oligonucleotide frequencies, as well as by separating models 2343 for bacteria and archaea. These advances have increased the accuracy of model 2344 reconstruction and, subsequently, gene prediction. We describe the refined 2345 method and assess its accuracy on known prokaryotic genomes split into short 2346 sequences. Also, we show that as a result of application of the new method, 2347 several thousands of new genes could be added to existing annotations of several 2348 human and mouse gut metagenomes.}, 2349 author = {Wenhan Zhu and Alexandre Lomsadze and Mark Borodovsky}, 2350 doi = {10.1093/nar}, 2351 journal = {Nucleic Acids Research}, 2352 number = {12}, 2353 pages = {e132}, 2354 title = {Ab initio gene identification in metagenomic sequences}, 2355 volume = {38}, 2356 year = {2010} 2357 } 2358 2359 @techreport{Fink-1995-conjugate-compendium, 2360 address = {Bozeman, Montana}, 2361 author = {Daniel Fink}, 2362 institution = {Environmental Statistics Group, Department of Biology, Montana State Univeristy}, 2363 title = {A Compendium of Conjugate Priors}, 2364 url = {http://www.people.cornell.edu/pages/df36/CONJINTRnewTEX.pdf}, 2365 year = {1995} 2366 } 2367 2368 @article{Zabell-1992, 2369 abstract = {A major difficulty for currently existing theories of 2370 inductive inference involves the question of what to do when novel, unknown, or 2371 previously unsuspected phenomena occur. In this paper one particular instance of 2372 this difficulty is considered, the so-called sampling of species problem. The 2373 classical probabilistic theories of inductive inference due to Laplace, Johnson, 2374 de Finetti, and Carnap adopt a model of simple enumerative induction in which 2375 there are a prespecified number of types or species which may be observed. But, 2376 realistically, this is often not the case. In 1838 the English mathematician 2377 Augustus De Morgan proposed a modification of the Laplacian model to accommodate 2378 situations where the possible types or species to be observed are not assumed to 2379 be known in advance; but he did not advance a justification for his solution. In 2380 this paper a general philosophical approach to such problems is suggested, 2381 drawing on work of the English mathematician J. F. C. Kingman. It then emerges 2382 that the solution advanced by De Morgan has a very deep, if not totally 2383 unexpected, justification. The key idea is that although lsquoexchangeablersquo 2384 random sequences are the right objects to consider when all possible 2385 outcome-types are known in advance, exchangeable random partitions are the right 2386 objects to consider when they are not. The result turns out to be very 2387 satisfying. The classical theory has several basic elements: a representation 2388 theorem for the general exchangeable sequence (the de Finetti representation 2389 theorem), a distinguished class of sequences (those employing Dirichlet priors), 2390 and a corresponding rule of succession (the continuum of inductive methods). The 2391 new theory has parallel basic elements: a representation theorem for the general 2392 exchangeable random partition (the Kingman representation theorem), a 2393 distinguished class of random partitions (the Poisson-Dirichlet process), and a 2394 rule of succession which corresponds to De Morgan's rule.}, 2395 annote = {ook op papier}, 2396 author = {Sandy L. Zabell}, 2397 doi = {10.1007/BF00485351}, 2398 journal = {Synthese}, 2399 localfile = {article/Zabell-1992.pdf}, 2400 number = {2}, 2401 pages = {205–232}, 2402 publisher = {Harvard Business School Publication Corp.}, 2403 title = {Predicting the unpredictable}, 2404 volume = {90}, 2405 year = {1992} 2406 } 2407 2408 @article{Inuiguchi-Ramik-2000, 2409 abstract = {In this paper, we review some fuzzy linear programming 2410 methods and techniques from a practical point of view. In the first part, the 2411 general history and the approach of fuzzy mathematical programming are 2412 introduced. Using a numerical example, some models of fuzzy linear programming 2413 are described. In the second part of the paper, fuzzy mathematical programming 2414 approaches are compared to stochastic programming ones. The advantages and 2415 disadvantages of fuzzy mathematical programming approaches are exemplified in 2416 the setting of an optimal portfolio selection problem. Finally, some newly 2417 developed ideas and techniques in fuzzy mathematical programming are briefly 2418 reviewed.}, 2419 author = {Masahiro Inuiguchi and Jaroslav Ramík}, 2420 doi = {10.1016/S0165-0114(98)00449-7}, 2421 issn = {0165-0114}, 2422 journal = {Fuzzy Sets and Systems}, 2423 keywords = {Fuzzy constraint; Fuzzy goal; Fuzzy mathematical programming; Necessity measure; Portfolio selection; Possibility measure; Simplex method; Stochastic programming}, 2424 localfile = {article/Inuiguchi-Ramik-2000.pdf}, 2425 number = {1}, 2426 pages = {3–28}, 2427 title = {Possibilistic linear programming: a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem}, 2428 volume = {111}, 2429 year = {2000} 2430 } 2431 2432 @book{Protein-Atlas-1978, 2433 editor = {M. O. Dayhoff}, 2434 title = {Atlas of Protein Sequence and Structure}, 2435 year = {1978} 2436 } 2437 2438 @article{Hart-MasColell-2001, 2439 author = {Sergiu Hart and Andreu Mas-Colell}, 2440 doi = {10.1006/jeth.2000.2746}, 2441 journal = {Journal of Economic Theory}, 2442 localfile = {article/Hart-MasColell-2001.pdf}, 2443 pages = {26–54}, 2444 title = {A General Class of Adaptive Strategies}, 2445 volume = {98}, 2446 year = {2001} 2447 } 2448 2449 @article{Couso-Moral-Walley-2000-independence, 2450 abstract = {Our aim in this paper is to clarify the notion of 2451 independence for imprecise probabilities. Suppose that two marginal experiments 2452 are each described by an imprecise probability model, i.e., by a convex set of 2453 probability distributions or an equivalent model such as upper and lower 2454 probabilities or previsions. Then there are several ways to define independence 2455 of the two experiments and to construct an imprecise probability model for the 2456 joint experiment. We survey and compare six definitions of independence. To 2457 clarify the meaning of the definitions and the relationships between them, we 2458 give simple examples which involve drawing balls from urns. For each concept of 2459 independence, we give a mathematical definition, an intuitive or behavioural 2460 interpretation, assumptions under which the definition is justified, and an 2461 example of an urn model to which the definition is applicable. Each of the 2462 independence concepts we study appears to be useful in some kinds of 2463 application. The concepts of strong independence and epistemic independence 2464 appear to be the most frequently applicable.}, 2465 author = {Inés Couso and Serafín Moral and Peter Walley}, 2466 doi = {10.1017/S1357530900000156}, 2467 journal = {Risk, Decision and Policy}, 2468 localfile = {article/Couso-Moral-Walley-2000-independence.pdf}, 2469 number = {2}, 2470 pages = {165–181}, 2471 title = {A survey of concepts of independence for imprecise probabilities}, 2472 volume = {5}, 2473 year = {2000} 2474 } 2475 2476 @article{DeCooman-2002, 2477 abstract = {Hierarchical models are rather common in uncertainty theory. 2478 They arise when there is a ‘correct’ or ‘ideal’ (the so-called first-order) 2479 uncertainty model about a phenomenon of interest, but the modeler is uncertain 2480 about what it is. The modeler's uncertainty is then called second-order 2481 uncertainty. For most of the hierarchical models in the literature, both the 2482 first- and the second-order models are precise, i.e., they are based on 2483 classical probabilities. In the present paper, I propose a specific hierarchical 2484 model that is imprecise at the second level, which means that at this level, 2485 lower probabilities are used. No restrictions are imposed on the underlying 2486 first-order model: that is allowed to be either precise or imprecise. I argue 2487 that this type of hierarchical model generalizes and includes a number of 2488 existing uncertainty models, such as imprecise probabilities, Bayesian models, 2489 and fuzzy probabilities. The main result of the paper is what I call 2490 precision–imprecision equivalence: the implications of the model for decision 2491 making and statistical reasoning are the same, whether the underlying 2492 first-order model is assumed to be precise or imprecise.}, 2493 annote = {reprint}, 2494 author = {Gert {De Cooman}}, 2495 doi = {10.1016/S0378-3758(01)00209-9}, 2496 journal = {Journal of Statistical Planning and Inference}, 2497 keywords = {coherence; hierarchical uncertainty model; imprecision; natural extension}, 2498 localfile = {article/DeCooman-2002.pdf}, 2499 number = {1}, 2500 pages = {175–198}, 2501 publisher = {Elsevier}, 2502 title = {Precision-imprecision equivalence in a broad class of imprecise hierarchical uncertainty models}, 2503 volume = {105}, 2504 year = {2002} 2505 } 2506 2507 @article{Buehler-1976, 2508 abstract = {De Finetti has defined coherent previsions and coherent 2509 probabilities, and others have described concepts of coherent actions or 2510 coherent decisions. Here we consider a related concept of coherent preferences. 2511 Willingness to accept one side of a bet is an example of a preference. A set of 2512 preferences is called incoherent if reversal of some subset yields a uniform 2513 increase in utility, as with a sure win for a collection of bets. In both 2514 probability and statistical models (where preferences are conditional on data) 2515 separating hyperplane theorems show that coherence implies existence of a 2516 probability measure from which the preferences could have been inferred. 2517 Relationships to confidence intervals and to decision theory are indicated. No 2518 single definition of coherence is given which covers all cases of interest. The 2519 various cases distinguish between probability and statistical models and between 2520 finite and infinite spaces. No satisfactory theory is given for continuous 2521 statistical models.}, 2522 annote = {ook op papier}, 2523 author = {Robert J. Buehler}, 2524 doi = {10.1214/aos}, 2525 issn = {0090-5364}, 2526 journal = {The Annals of Statistics}, 2527 localfile = {article/Buehler-1976.pdf}, 2528 number = {6}, 2529 pages = {1051–1064}, 2530 publisher = {Institute of Mathematical Statistics}, 2531 title = {Coherent preferences}, 2532 url = {http://www.jstor.org/stable/2958578}, 2533 volume = {4}, 2534 year = {1976} 2535 } 2536 2537 @book{Michie-Spiegelhalter-Taylor-1994, 2538 editor = {D. Michie and D. J. Spiegelhalter and C. C. Taylor}, 2539 title = {Machine Learning, Neural and Statistical Classification}, 2540 url = {http://www.amsta.leeds.ac.uk/~charles/statlog}, 2541 year = {1994} 2542 } 2543 2544 @article{Kadane-Larkey-1982-reply, 2545 annote = {ook op papier}, 2546 author = {Joseph B. Kadane and Patrick D. Larkey}, 2547 doi = {10.1287/mnsc.28.2.124}, 2548 journal = {Management Science}, 2549 localfile = {article/Kadane-Larkey-1982-reply.pdf}, 2550 number = {2}, 2551 pages = {124}, 2552 publisher = {INFORMS}, 2553 title = {Reply to Professor Harsanyi}, 2554 url = {http://repository.cmu.edu/statistics/38}, 2555 volume = {28}, 2556 year = {1982} 2557 } 2558 2559 @article{Zaffalon-Fagiuoli-2003, 2560 abstract = {Bayesian networks are models for uncertain reasoning which 2561 are achieving a growing importance also for the data mining task of 2562 classification. Credal networks extend Bayesian nets to sets of distributions, 2563 or credal sets. This paper extends a state-of-the-art Bayesian net for 2564 classification, called tree-augmented naive Bayes classifier, to credal sets 2565 originated from probability intervals. This extension is a basis to address the 2566 fundamental problem of prior ignorance about the distribution that generates the 2567 data, which is a commonplace in data mining applications. This issue is often 2568 neglected, but addressing it properly is a key to ultimately draw reliable 2569 conclusions from the inferred models. In this paper we formalize the new model, 2570 develop an exact linear-time classification algorithm, and evaluate the credal 2571 net-based classifier on a number of real data sets. The empirical analysis shows 2572 that the new classifier is good and reliable, and raises a problem of excessive 2573 caution that is discussed in the paper. Overall, given the favorable trade-off 2574 between expressiveness and efficient computation, the newly proposed classifier 2575 appears to be a good candidate for the wide-scale application of reliable 2576 classifiers based on credal networks, to real and complex tasks.}, 2577 author = {Marco Zaffalon and Enrico Fagiuoli}, 2578 doi = {10.1023/A:1025822321743}, 2579 journal = {Reliable Computing}, 2580 number = {6}, 2581 pages = {487–509}, 2582 title = {Tree-Based Credal Networks for Classification}, 2583 volume = {9}, 2584 year = {2003} 2585 } 2586 2587 @article{BenTal-Nemirovski-2002, 2588 abstract = {Robust Optimization (RO) is a modeling methodology, combined 2589 with computational tools, to process optimization problems in which the data are 2590 uncertain and is only known to belong to some uncertainty set. The paper surveys 2591 the main results of RO as applied to uncertain linear, conic quadratic and 2592 semidefinite programming. For these cases, computationally tractable robust 2593 counterparts of uncertain problems are explicitly obtained, or good 2594 approximations of these counterparts are proposed, making RO a useful tool for 2595 real-world applications. We discuss some of these applications, specifically: 2596 antenna design, truss topology design and stability analysis/synthesis in 2597 uncertain dynamic systems. We also describe a case study of 90 LPs from the 2598 NETLIB collection. The study reveals that the feasibility properties of the 2599 usual solutions of real world LPs can be severely affected by small 2600 perturbations of the data and that the RO methodology can be successfully used 2601 to overcome this phenomenon.}, 2602 author = {Aharon Ben-Tal and Arkadi Nemirovski}, 2603 doi = {10.1007/s101070100286}, 2604 issn = {0025-5610}, 2605 journal = {Mathematical Programming}, 2606 localfile = {article/BenTal-Nemirovski-2002.pdf}, 2607 number = {3}, 2608 pages = {453–480}, 2609 publisher = {Springer}, 2610 title = {Robust optimization – methodology and applications}, 2611 volume = {92}, 2612 year = {2002} 2613 } 2614 2615 @article{Morris-1982, 2616 author = {Carl N. Morris}, 2617 doi = {10.1214/aos}, 2618 journal = {The Annals of Statistics}, 2619 localfile = {article/Morris-1982.pdf}, 2620 number = {1}, 2621 pages = {65–80}, 2622 publisher = {Institute of Mathematical Statistics}, 2623 title = {Natural exponential families with quadratic variance functions}, 2624 volume = {10}, 2625 year = {1982} 2626 } 2627 2628 @article{Krogh-etal-1994, 2629 abstract = {Hidden Markov Models (HMMs) are applied to the problems of 2630 statistical modeling, database searching and multiple sequence alignment of 2631 protein families and protein domains. These methods are demonstrated on the 2632 globin family, the protein kinase catalytic domain, and the EF-hand calcium 2633 binding motif. In each case the parameters of an HMM are estimated from a 2634 training set of unaligned sequences. After the HMM is built, it is used to 2635 obtain a multiple alignment of all the training sequences. It is also used to 2636 search the SWISS-PROT 22 database for other sequences that are members of the 2637 given protein family, or contain the given domain. The HMM produces multiple 2638 alignments of good quality that agree closely with the alignments produced by 2639 programs that incorporate three-dimensional structural information. When 2640 employed in discrimination tests (by examining how closely the sequences in a 2641 database fit the globin, kinase and EF-hand HMMs), the HMM is able to 2642 distinguish members of these families from non-members with a high degree of 2643 accuracy. Both the HMM and PROFILESEARCH (a technique used to search for 2644 relationships between a protein sequence and multiply aligned sequences) perform 2645 better in these tests than PROSITE (a dictionary of sites and patterns in 2646 proteins). The HMM appears to have a slight advantage over PROFILESEARCH in 2647 terms of lower rates of false negatives and false positives, even though the HMM 2648 is trained using only unaligned sequences, whereas PROFILESEARCH requires 2649 aligned training sequences. Our results suggest the presence of an EF-hand 2650 calcium binding motif in a highly conserved and evolutionary preserved putative 2651 intracellular region of 155 residues in the [alpha]-1 subunit of L-type calcium 2652 channels which play an important role in excitation-contraction coupling. This 2653 region has been suggested to contain the functional domains that are typical or 2654 essential for all L-type calcium channels regardless of whether they couple to 2655 ryanodine receptors, conduct ions or both.}, 2656 author = {Anders Krogh and Michael Brown and I. Saira Mian and Kimmen Sjölander and David Haussler}, 2657 doi = {10.1006/jmbi.1994.1104}, 2658 issn = {0022-2836}, 2659 journal = {Journal of Molecular Biology}, 2660 keywords = {EF-hand; globin; hidden Markov models; kinase}, 2661 localfile = {article/Krogh-etal-1994.pdf}, 2662 number = {5}, 2663 pages = {1501–1531}, 2664 title = {Hidden Markov models in computational biology: Applications to protein modeling}, 2665 volume = {235}, 2666 year = {1994} 2667 } 2668 2669 @article{Diaconis-Freedman-1980-partial-xch, 2670 author = {Persi Diaconis and D. Freedman}, 2671 doi = {10.1214/aop}, 2672 journal = {The Annals of Probability}, 2673 localfile = {article/Diaconis-Freedman-1980-partial-xch.pdf}, 2674 number = {1}, 2675 pages = {115–130}, 2676 title = {De Finetti's theorem for Markov chains}, 2677 url = {http://www.jstor.org/stable/2243063}, 2678 volume = {8}, 2679 year = {1980} 2680 } 2681 2682 @techreport{Murphy-2001-graphical, 2683 author = {Kevin P. Murphy}, 2684 institution = {University of British Columbia}, 2685 title = {An introduction to graphical models}, 2686 url = {http://people.cs.ubc.ca/~murphyk/Papers/intro_gm.pdf}, 2687 year = {2001} 2688 } 2689 2690 @book{Huzurbazar-1976, 2691 address = {New York}, 2692 author = {Vasant S. Huzurbazar}, 2693 editor = {Anant M. Kshirsagar}, 2694 publisher = {Marcel Dekker}, 2695 series = {Statistics: Textbooks and Monographs}, 2696 title = {Sufficient Statistics: Selected Contributions}, 2697 volume = {19}, 2698 year = {1976} 2699 } 2700 2701 @article{Kadane-Schervish-Seidenfeld-1996, 2702 abstract = {When can a Bayesian select an hypothesis H and design an 2703 experiment (or a sequence of experiments) to make certain that, given the 2704 experimental outcome(s), the posterior probability of H will be greater than its 2705 prior probability? We discuss an elementary result that establishes sufficient 2706 conditions under which this reasoning to a foregone conclusion cannot occur. We 2707 illustrate how when the sufficient conditions fail, because probability is 2708 finitely but not countably additive, it may be that a Bayesian can design an 2709 experiment to lead his/her posterior probability into a foregone conclusion. The 2710 problem has a decision theoretic version in which a Bayesian might rationally 2711 pay not to see the outcome of certain cost-free experiments, which we discuss 2712 from several perspectives. Also, we relate this issue in Bayesian hypothesis 2713 testing to various concerns about "optional stopping."}, 2714 author = {Joseph B. Kadane and Mark J. Schervish and Teddy Seidenfeld}, 2715 issn = {0162-1459}, 2716 journal = {Journal of the American Statistical Association}, 2717 keywords = {coherence; finite additivity; sequential tests; stopping rules; value of information}, 2718 localfile = {article/Kadane-Schervish-Seidenfeld-1996-foregone.pdf}, 2719 month = sep, 2720 number = {435}, 2721 pages = {1228–1235}, 2722 publisher = {American Statistical Association}, 2723 title = {Reasoning to a foregone conclusion}, 2724 url = {http://www.jstor.org/stable/2291741}, 2725 volume = {91}, 2726 year = {1996} 2727 } 2728 2729 @inproceedings{Quaeghebeur-DeCooman-2003-games, 2730 address = {Waterloo, Ontario, Canada}, 2731 author = {Erik Quaeghebeur and Gert {De Cooman}}, 2732 booktitle = {ISIPTA '03: Proceedings of the Third International Symposium on Imprecise Probabilities and Their Applications}, 2733 editor = {Jean-Marc Bernard and Teddy Seidenfeld and Marco Zaffalon}, 2734 location = {Lugano, Switzerland}, 2735 pages = {452–466}, 2736 publisher = {Carleton Scientific}, 2737 series = {Proceedings in Informatics}, 2738 title = {Game-Theoretic Learning Using the Imprecise Dirichlet Model}, 2739 volume = {18}, 2740 year = {2003} 2741 } 2742 2743 @article{Moral-2005-desir, 2744 abstract = {This paper studies graphoid properties for epistemic 2745 irrelevance in sets of desirable gambles. For that aim, the basic operations of 2746 conditioning and marginalization are expressed in terms of variables. Then, it 2747 is shown that epistemic irrelevance is an asymmetric graphoid. The intersection 2748 property is verified in probability theory when the global probability 2749 distribution is positive in all the values. Here it is always verified due to 2750 the handling of zero probabilities in sets of gambles. An asymmetrical 2751 D-separation principle is also presented, by which this type of independence 2752 relationships can be represented in directed acyclic graphs.}, 2753 annote = {ook op papier}, 2754 author = {Serafín Moral}, 2755 doi = {10.1007/s10472-005-9011-0}, 2756 journal = {Annals of Mathematics and Artificial Intelligence}, 2757 keywords = {Desirable gambles; conditioning; epistemic independence; epistemic irrelevance; imprecise probabilities}, 2758 localfile = {article/Moral-2005-desir.pdf}, 2759 pages = {197–214}, 2760 title = {Epistemic irrelevance on sets of desirable gambles}, 2761 volume = {45}, 2762 year = {2005} 2763 } 2764 2765 @techreport{Schervish-Seidenfeld-Kadane-1998, 2766 author = {Mark J. Schervish and Teddy Seidenfeld and Joseph B. Kadane}, 2767 institution = {Carnegie Mellon University}, 2768 number = {660}, 2769 title = {Two Measures of Incoherence: How Not to Gamble If You Must}, 2770 url = {http://www.stat.cmu.edu/tr/tr660/tr660.html}, 2771 year = {1998} 2772 } 2773 2774 @article{Buckley-Qu-1991, 2775 author = {J. J. Buckley and Y. Qu}, 2776 doi = {10.1016/0165-0114(91)90019-M}, 2777 journal = {Fuzzy Sets and Systems}, 2778 keywords = {algebra; fuzzy number}, 2779 localfile = {article/Buckley-Qu-1991.pdf}, 2780 number = {1}, 2781 pages = {33–43}, 2782 publisher = {Elsevier}, 2783 title = {Solving systems of linear fuzzy equations}, 2784 volume = {43}, 2785 year = {1991} 2786 } 2787 2788 @article{Dyer-1983, 2789 abstract = {The computational complexity of problems relating to the 2790 enumeration of all the vertices of a convex polyhedron defined by linear 2791 inequalities is examined. Several published approaches are evaluated in this 2792 light. A new algorithm is described, and shown to have a better complexity 2793 estimate than existing methods. Empirical evidence supporting the theoretical 2794 superiority is presented. Finally vertex enumeration is discussed when the space 2795 containing the polyhedra is of fixed dimension and only the size of the 2796 inequality system is permitted to vary.}, 2797 author = {M. E. Dyer}, 2798 issn = {0364-765X}, 2799 journal = {Mathematics of Operations Research}, 2800 localfile = {article/Dyer-1983.pdf}, 2801 number = {3}, 2802 pages = {381–402}, 2803 publisher = {INFORMS}, 2804 title = {The complexity of vertex enumeration methods}, 2805 url = {http://www.jstor.org/stable/3689308}, 2806 volume = {8}, 2807 year = {1983} 2808 } 2809 2810 @phdthesis{Quaeghebeur-2010-phd, 2811 author = {Liesbet Quaeghebeur}, 2812 school = {Universiteit Antwerpen}, 2813 title = {A Philosophy of Everyday, Face-to-face Conversation}, 2814 year = {2010} 2815 } 2816 2817 @book{Dubois-Prade-1988, 2818 address = {Paris}, 2819 author = {Didier Dubois and Henri Prade}, 2820 edition = {2}, 2821 publisher = {Masson}, 2822 title = {Théorie des possibilités: applications à la représentation des connaissances en informatique}, 2823 year = {1988} 2824 } 2825 2826 @article{Soyster-1973, 2827 abstract = {This note formulates a convex mathematical programming 2828 problem in which the usual definition of the feasible region is replaced by a 2829 significantly different strategy. Instead of specifying the feasible region by a 2830 set of convex inequalities, fi(x)≤ bi, i=1,2,⋯,m, the feasible region is defined 2831 via set containment. Here n convex activity sets {Kj, j=1,2,⋯,n} and a convex 2832 resource set K are specified and the feasible region is given by X={x ∈ 2833 R^{n}|x\_{1}K\_{1}+x\_{2}K\_{2}+⋯ +x\_{n}K\_{n}\subseteq K,\ x\_{j}\geq 0}, 2834 where the binary operation + refers to addition of sets. The problem is then to 2835 find x∈ X that maximizes the linear function c· x. When the resource set has a 2836 special form, this problem is solved via an auxiliary linear-programming problem 2837 and application to inexact linear programming is possible.}, 2838 author = {A.L. L. Soyster}, 2839 issn = {0030-364X}, 2840 journal = {Operations Research}, 2841 localfile = {article/Soyster-1973.pdf}, 2842 number = {5}, 2843 pages = {1154–1157}, 2844 publisher = {INFORMS}, 2845 title = {Convex programming with set-inclusive constraints and applications to inexact linear programming}, 2846 url = {http://www.jstor.org/stable/168933}, 2847 volume = {21}, 2848 year = {1973} 2849 } 2850 2851 @article{GutierrezPena-Smith-1997-review, 2852 author = {Eduardo Gutiérrez-Peña and Adrian F. M. Smith}, 2853 doi = {10.1007/BF02564426}, 2854 journal = {Test}, 2855 localfile = {article/GutierrezPena-Smith-1997-review.pdf}, 2856 number = {1}, 2857 pages = {1–90}, 2858 publisher = {Springer}, 2859 title = {Exponential and Bayesian conjugate families: review and extensions}, 2860 volume = {6}, 2861 year = {1997} 2862 } 2863 2864 @article{vonNeumann-1928, 2865 author = {John von Neumann}, 2866 doi = {10.1007/BF01448847}, 2867 journal = {Mathematische Annalen}, 2868 localfile = {article/vonNeumann-1928.pdf}, 2869 number = {1}, 2870 pages = {295–320}, 2871 title = {Zur Theorie der Gesellschaftsspiele}, 2872 volume = {100}, 2873 year = {1928} 2874 } 2875 2876 @inproceedings{Miranda-Troffaes-destercke-2008-SMPS, 2877 annote = {extended version on paper; available from authors}, 2878 author = {Enrique Miranda and Matthias C. M. Troffaes and Sébastien Destercke}, 2879 booktitle = {SMPS}, 2880 doi = {10.1007/978-3-540-85027-4_29}, 2881 editor = {Didier Dubois and María Asunción Lubiano and Henri Prade and María Angeles Gil and Przemysław Grzegorzewski and Olgierd Hryniewicz}, 2882 isbn = {978-3-540-85026-7}, 2883 pages = {235–242}, 2884 publisher = {Springer}, 2885 series = {Advances in Soft Computing}, 2886 title = {Generalised p-Boxes on Totally Ordered Spaces}, 2887 volume = {48}, 2888 year = {2008} 2889 } 2890 2891 @techreport{Fioretti-2001-Shackle, 2892 abstract = {Evidence Theory is a branch of mathematics that concerns the 2893 combination of empirical evidence in an individual's mind in order to construct 2894 a coherent picture of reality. Designed to deal with unexpected empirical 2895 evidence suggesting new possibilities, evidence theory has a lot in common with 2896 Shackle's idea of decision-making as a creative act. This essay investigates 2897 this connection in detail, pointing to the usefulness of evidence theory to 2898 formalise and extend Shackle's decision theory. In order to ease a proper 2899 framing of the issues involved, evidence theory is not only compared with 2900 Shackle's ideas but also with additive and sub-additive probability theories. 2901 Furthermore, the presentation of evidence theory does not refer to the original 2902 version only, but takes account of its most recent developments, too.}, 2903 author = {Guido Fioretti}, 2904 institution = {Università di Firenze and ICER, Torino}, 2905 title = {A mathematical theory of evidence for G. L. S. Shackle}, 2906 year = {2001} 2907 } 2908 2909 @phdthesis{Kriegler-2005, 2910 author = {Elmar Kriegler}, 2911 school = {Universität Potsdam}, 2912 title = {Imprecise Probability Analysis for Integrated Assessment of Climate Change}, 2913 year = {2005} 2914 } 2915 2916 @inproceedings{Williams-1974, 2917 author = {Peter M. Williams}, 2918 booktitle = {Formal methods in the methodology of empirical sciences: Proceedings of the conference for formal methods in the methodology of empirical sciences}, 2919 editor = {Marian Przełęcki and Klemens Szaniawski and Ryszard Wójcicki}, 2920 pages = {229–246}, 2921 publisher = {D. Reidel Publishing Company and Ossolineum Publishing company}, 2922 title = {Indeterminate probabilities}, 2923 year = {1974} 2924 } 2925 2926 @article{Antonucci-Zaffalon-2008, 2927 abstract = {Credal networks are models that extend Bayesian nets to deal 2928 with imprecision in probability, and can actually be regarded as sets of 2929 Bayesian nets. Credal nets appear to be powerful means to represent and deal 2930 with many important and challenging problems in uncertain reasoning. We give 2931 examples to show that some of these problems can only be modeled by credal nets 2932 called non-separately specified. These, however, are still missing a graphical 2933 representation language and updating algorithms. The situation is quite the 2934 opposite with separately specified credal nets, which have been the subject of 2935 much study and algorithmic development. This paper gives two major 2936 contributions. First, it delivers a new graphical language to formulate any type 2937 of credal network, both separately and non-separately specified. Second, it 2938 shows that any non-separately specified net represented with the new language 2939 can be easily transformed into an equivalent separately specified net, defined 2940 over a larger domain. This result opens up a number of new outlooks and concrete 2941 outcomes: first of all, it immediately enables the existing algorithms for 2942 separately specified credal nets to be applied to non-separately specified ones. 2943 We explore this possibility for the 2U algorithm: an algorithm for exact 2944 updating of singly connected credal nets, which is extended by our results to a 2945 class of non-separately specified models. We also consider the problem of 2946 inference on Bayesian networks, when the reason that prevents some of the 2947 variables from being observed is unknown. The problem is first reformulated in 2948 the new graphical language, and then mapped into an equivalent problem on a 2949 separately specified net. This provides a first algorithmic approach to this 2950 kind of inference, which is also proved to be NP-hard by similar transformations 2951 based on our formalism.}, 2952 author = {Alessandro Antonucci and Marco Zaffalon}, 2953 doi = {10.1016/j.ijar.2008.02.005}, 2954 issn = {0888-613X}, 2955 journal = {International Journal of Approximate Reasoning}, 2956 keywords = {Bayesian networks; Conservative inference rule; Conservative updating; Credal networks; Credal sets; Imprecise probabilities; Probabilistic graphical models}, 2957 localfile = {article/Antonucci-Zaffalon-2008.pdf}, 2958 number = {2}, 2959 pages = {345–361}, 2960 title = {Decision-theoretic specification of credal networks: A unified language for uncertain modeling with sets of Bayesian networks}, 2961 volume = {49}, 2962 year = {2008} 2963 } 2964 2965 @article{Kschischang-Frey-Loeliger-2001, 2966 abstract = {Algorithms that must deal with complicated global functions 2967 of many variables often exploit the manner in which the given functions factor 2968 as a product of ldquo;local rdquo; functions, each of which depends on a subset 2969 of the variables. Such a factorization can be visualized with a bipartite graph 2970 that we call a factor graph, In this tutorial paper, we present a generic 2971 message-passing algorithm, the sum-product algorithm, that operates in a factor 2972 graph. Following a single, simple computational rule, the sum-product algorithm 2973 computes-either exactly or approximately-various marginal functions derived from 2974 the global function. A wide variety of algorithms developed in artificial 2975 intelligence, signal processing, and digital communications can be derived as 2976 specific instances of the sum-product algorithm, including the forward/backward 2977 algorithm, the Viterbi algorithm, the iterative ldquo;turbo rdquo; decoding 2978 algorithm, Pearl's (1988) belief propagation algorithm for Bayesian networks, 2979 the Kalman filter, and certain fast Fourier transform (FFT) algorithms}, 2980 author = {F. R. Kschischang and B. J. Frey and H.-A. Loeliger}, 2981 doi = {10.1109/18.910572}, 2982 issn = {0018-9448}, 2983 journal = {IEEE Transactions on Information Theory}, 2984 keywords = {Bayesian networks; FFT algorithms; HMM; Kalman filter; Kalman filters; Viterbi algorithm; Viterbi decoding; artificial intelligence; belief networks; belief propagation algorithm; bipartite graph; computational rule; digital communication; digital communications; factor graphs; factorization; fast Fourier transform; fast Fourier transforms; forward/backward algorithm; functional analysis; generic message-passing algorithm; global function; global functions; graph theory; hidden Markov models; iterative decoding; iterative turbo decoding algorithm; local functions; marginal functions; message passing; signal processing; sum-product algorithm; turbo codes}, 2985 localfile = {article/Kschischang-Frey-Loeliger-2001.pdf}, 2986 number = {2}, 2987 pages = {498–519}, 2988 title = {Factor graphs and the sum-product algorithm}, 2989 volume = {47}, 2990 year = {2001} 2991 } 2992 2993 @article{Seidenfeld-1985, 2994 abstract = {Can there be good reasons for judging one set of 2995 probabilistic assertions more reliable than a second? There are many candidates 2996 for measuring "goodness" of probabilistic forecasts. Here, I focus on one such 2997 aspirant: calibration. Calibration requires an alignment of announced 2998 probabilities and observed relative frequency, e.g., 50 percent of forecasts 2999 made with the announced probability of .5 occur, 70 percent of forecasts made 3000 with probability .7 occur, etc. To summarize the conclusions: (i) Surveys 3001 designed to display calibration curves, from which a recalibration is to be 3002 calculated, are useless without due consideration for the interconnections 3003 between questions (forecasts) in the survey. (ii) Subject to feedback, 3004 calibration in the long run is otiose. It gives no ground for validating one 3005 coherent opinion over another as each coherent forecaster is (almost) sure of 3006 his own long-run calibration. (iii) Calibration in the short run is an 3007 inducement to hedge forecasts. A calibration score, in the short run, is 3008 improper. It gives the forecaster reason to feign violation of total evidence by 3009 enticing him to use the more predictable frequencies in a larger finite 3010 reference class than that directly relevant.}, 3011 author = {Teddy Seidenfeld}, 3012 journal = {Philosophy of Science}, 3013 localfile = {article/Seidenfeld-1985.pdf}, 3014 number = {2}, 3015 pages = {274–294}, 3016 title = {Calibration, coherence, and scoring rules}, 3017 url = {http://www.jstor.org/stable/187511}, 3018 volume = {52}, 3019 year = {1985} 3020 } 3021 3022 @book{DeFinetti-1970-book, 3023 author = {Bruno de Finetti}, 3024 publisher = {Giulio Einaudi}, 3025 title = {Teoria Delle Probabilità}, 3026 year = {1970} 3027 } 3028 3029 @article{Avis-Fukuda-1992, 3030 author = {David Avis and Komei Fukuda}, 3031 doi = {10.1007/BF02293050}, 3032 journal = {Discrete \& Computational Geometry}, 3033 localfile = {article/Avis-Fukuda-1992.pdf}, 3034 number = {1}, 3035 pages = {295–313}, 3036 publisher = {Springer}, 3037 title = {A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra}, 3038 url = {http://www.digizeitschriften.de/dms/img/?PPN=GDZPPN000365548}, 3039 volume = {8}, 3040 year = {1992} 3041 } 3042 3043 @article{Georgakopoulos-Kavvadias-Papadimitriou-1988, 3044 annote = {ook op papier}, 3045 author = {George Georgakopoulos and Dimitris Kavvadias and Christos H. Papadimitriou}, 3046 doi = {10.1016/0885-064X(88)90006-4}, 3047 journal = {Journal of Complexity}, 3048 localfile = {article/Georgakopoulos-Kavvadias-Papadimitriou-1988.pdf}, 3049 number = {1}, 3050 pages = {1–11}, 3051 publisher = {Elsevier}, 3052 title = {Probabilistic satisfiability}, 3053 volume = {4}, 3054 year = {1988} 3055 } 3056 3057 @incollection{Jimenez-etal-2005, 3058 author = {F. Jiménez and G. Sánchez and J. Cadenas and A. Gómez-Skarmeta and J. Verdegay}, 3059 booktitle = {Computational Intelligence, Theory and Applications}, 3060 doi = {10.1007/3-540-31182-3_66}, 3061 editor = {Bernd Reusch}, 3062 isbn = {978-3-540-22807-3}, 3063 localfile = {incollection/Jimenez-etal-2005.pdf}, 3064 pages = {713–722}, 3065 publisher = {Springer}, 3066 series = {Advances in Soft Computing}, 3067 title = {Nonlinear Optimization with Fuzzy Constraints by Multi-Objective Evolutionary Algorithms}, 3068 volume = {33}, 3069 year = {2005} 3070 } 3071 3072 @article{Ide-Cozman-2008, 3073 abstract = {This paper presents a family of algorithms for approximate 3074 inference in credal networks (that is, models based on directed acyclic graphs 3075 and set-valued probabilities) that contain only binary variables. Such networks 3076 can represent incomplete or vague beliefs, lack of data, and disagreements among 3077 experts; they can also encode models based on belief functions and possibilistic 3078 measures. All algorithms for approximate inference in this paper rely on exact 3079 inferences in credal networks based on polytrees with binary variables, as these 3080 inferences have polynomial complexity. We are inspired by approximate algorithms 3081 for Bayesian networks; thus the Loopy 2U algorithm resembles Loopy Belief 3082 Propagation, while the Iterated Partial Evaluation and Structured Variational 2U 3083 algorithms are, respectively, based on Localized Partial Evaluation and 3084 variational techniques.}, 3085 author = {Jaime Shinsuke Ide and Fabio Gagliardi Cozman}, 3086 doi = {10.1016/j.ijar.2007.09.003}, 3087 issn = {0888-613X}, 3088 journal = {International Journal of Approximate Reasoning}, 3089 keywords = {2U algorithm; Credal networks; Loopy Belief Propagation; Variational methods}, 3090 localfile = {article/Ide-Cozman-2008.pdf}, 3091 number = {1}, 3092 pages = {275–296}, 3093 title = {Approximate algorithms for credal networks with binary variables}, 3094 volume = {48}, 3095 year = {2008} 3096 } 3097 3098 @article{Milne-1993, 3099 abstract = {Taking as starting point two familiar interpretations of 3100 probability, we develop these in a perhaps unfamiliar way to arrive ultimately 3101 at an improbable claim concerning the proper axiomatization of probability 3102 theory: the domain of definition of a point-valued probability distribution is 3103 an orthomodular partially ordered set. Similar claims have been made in the 3104 light of quantum mechanics but here the motivation is intrinsically 3105 probabilistic. This being so the main task is to investigate what light, if any, 3106 this sheds on quantum mechanics. In particular it is important to know under 3107 what conditions these point-valued distributions can be thought of as derived 3108 from distribution-pairs of upper and lower probabilities on boolean algebras. 3109 Generalising known results this investigation unsurprisingly proves unrewarding. 3110 In the light of this failure the next topic investigated is how these 3111 generalized probability distributions are to be interpreted.}, 3112 author = {Peter Milne}, 3113 doi = {10.1007/BF01049259}, 3114 journal = {Journal of Philosophical Logic}, 3115 pages = {129–168}, 3116 title = {The foundations of probability and quantum mechanics}, 3117 volume = {22}, 3118 year = {1993} 3119 } 3120 3121 @article{Dietzenbacher-1994-Perron-Frobenius, 3122 abstract = {The dominant eigenvalue and the corresponding eigenvector 3123 (or Perron vector) of a non-linear eigensystem are considered. We discuss the 3124 effects upon these, of perturbations and of aggregation of the underlying 3125 mapping. The results are applied to study the sensitivity of the outputs in a 3126 non-linear input-output model. For that purpose, it is shown that the 3127 input-output model can be rewritten as a non-linear eigensystem. It turns out 3128 that the Perron vector of this eigensystem includes the solution vector of the 3129 input-output model.}, 3130 author = {Erik Dietzenbacher}, 3131 doi = {10.1016/0304-4068(94)90033-7}, 3132 journal = {Journal of Mathematical Economics}, 3133 localfile = {article/Dietzenbacher-1994-Perron-Frobenius.pdf}, 3134 number = {1}, 3135 pages = {21–31}, 3136 publisher = {Elsevier}, 3137 title = {The non-linear Perron-Frobenius theorem: Perturbations and aggregation}, 3138 volume = {23}, 3139 year = {1994} 3140 } 3141 3142 @inproceedings{Quaeghebeur-DeCooman-2004, 3143 address = {Helvoirt, The Netherlands}, 3144 author = {Erik Quaeghebeur and Gert {De Cooman}}, 3145 booktitle = {Book of Abstracts 23rd Benelux Meeting on Systems and Control}, 3146 editor = {Bram de Jager and Vincent Verdult}, 3147 pages = {113}, 3148 title = {Command line completion: an illustration of learning and decision making using the imprecise Dirichlet model}, 3149 year = {2004} 3150 } 3151 3152 @article{DeCampos-Huete-Moral-1994-intervals, 3153 abstract = {We study probability intervals as an interesting tool to 3154 represent uncertain information. A number of basic operations necessary to 3155 develop a calculus with probability intervals, such as combination, 3156 marginalization, conditioning and integration are studied in detail. Moreover, 3157 probability intervals are compared with other uncertainty theories, such as 3158 lower and upper probabilities, Choquet capacities of order two and belief and 3159 plausibility functions. The advantages of probability intervals with respect to 3160 these formalisms in computational efficiency are also highlighted.}, 3161 annote = {op papier}, 3162 author = {Luis M. de Campos and Juan F. Huete and Serafín Moral}, 3163 doi = {10.1142/S0218488594000146}, 3164 journal = {International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems}, 3165 keywords = {Combination; Conditioning; Lower and Upper Probability; Marginalization; Probability Intervals; Uncertainty Management}, 3166 localfile = {article/DeCampos-Huete-Moral-1994-intervals.pdf}, 3167 number = {2}, 3168 pages = {167–196}, 3169 title = {Probability intervals: a tool for uncertain reasoning}, 3170 url = {http://decsai.ugr.es/~lci/journal-papers-pdf/ijuf94.pdf}, 3171 volume = {2}, 3172 year = {1994} 3173 } 3174 3175 @article{DeCooman-Hermans-2008-bridging, 3176 abstract = {We give an overview of two approaches to probability theory 3177 where lower and upper probabilities, rather than probabilities, are used: 3178 Walley's behavioural theory of imprecise probabilities, and Shafer and Vovk's 3179 game-theoretic account of probability. We show that the two theories are more 3180 closely related than would be suspected at first sight, and we establish a 3181 correspondence between them that (i) has an interesting interpretation, and (ii) 3182 allows us to freely import results from one theory into the other. Our approach 3183 leads to an account of probability trees and random processes in the framework 3184 of Walley's theory. We indicate how our results can be used to reduce the 3185 computational complexity of dealing with imprecision in probability trees, and 3186 we prove an interesting and quite general version of the weak law of large 3187 numbers.}, 3188 author = {Gert {De Cooman} and Filip Hermans}, 3189 doi = {10.1016/j.artint.2008.03.001}, 3190 journal = {Artificial Intelligence}, 3191 keywords = {Coherence; Conglomerability; Event tree; Game-theoretic probability; Hoeffding’s inequality; Immediate prediction; Imprecise probabilities; Imprecise probability tree; Law of large numbers; Lower prevision; Markov chain; Prequential Principle; Probability tree; Random process}, 3192 localfile = {article/DeCooman-Hermans-2008-bridging.pdf}, 3193 number = {11}, 3194 pages = {1400–1427}, 3195 publisher = {Elsevier}, 3196 title = {Imprecise probability trees: Bridging two theories of imprecise probability}, 3197 volume = {172}, 3198 year = {2008} 3199 } 3200 3201 @article{DeCooman-Quaeghebeur-Miranda-2007-exchangeable, 3202 author = {Gert {De Cooman} and Erik Quaeghebeur and Enrique Miranda}, 3203 doi = {10.3150/09-BEJ182}, 3204 journal = {Bernoulli}, 3205 number = {3}, 3206 pages = {721–735}, 3207 title = {Exchangeable lower previsions}, 3208 volume = {15}, 3209 year = {2009} 3210 } 3211 3212 @article{Billingsley-1961, 3213 abstract = {This paper is an expository survey of the mathematical 3214 aspects of statistical inference as it applies to finite Markov chains, the 3215 problem being to draw inferences about the transition probabilities from one 3216 long, unbroken observation {x\_1, x\_2, ⋯, x\_n} on the chain. The topics 3217 covered include Whittle's formula, chi-square and maximum-likelihood methods, 3218 estimation of parameters, and multiple Markov chains. At the end of the paper it 3219 is briefly indicated how these methods can be applied to a process with an 3220 arbitrary state space or a continuous time parameter. Section 2 contains a 3221 simple proof of Whittle's formula; Section 3 provides an elementary and 3222 self-contained development of the limit theory required for the application of 3223 chi-square methods to finite chains. In the remainder of the paper, the results 3224 are accompanied by references to the literature, rather than by complete proofs. 3225 As is usual in a review paper, the emphasis reflects the author's interests. 3226 Other general accounts of statistical inference on Markov processes will be 3227 found in Grenander [53], Bartlett [9] and [10], Fortet [35], and in my monograph 3228 [18]. I would like to thank Paul Meier for a number of very helpful discussions 3229 on the topics treated in this paper, particularly those of Section 3.}, 3230 annote = {geannoteerde kopie}, 3231 author = {Patrick Billingsley}, 3232 journal = {The Annals of Mathematical Statistics}, 3233 localfile = {article/Billingsley-1961.pdf}, 3234 number = {1}, 3235 pages = {12–40}, 3236 title = {Statistical methods in Markov chains}, 3237 url = {http://www.jstor.org/stable/2237603}, 3238 volume = {32}, 3239 year = {1961} 3240 } 3241 3242 @article{Augustin-Coolen-2004, 3243 abstract = {The assumption A(n), proposed by Hill (J. Amer. Statist. 3244 Assoc. 63 (1968) 677), provides a natural basis for low structure non-parametric 3245 predictive inference, and has been justified in the Bayesian framework. This 3246 paper embeds A(n)-based inference into the theory of interval probability, by 3247 showing that the corresponding bounds are totally monotone F-probability and 3248 coherent. Similar attractive internal consistency results are proven to hold for 3249 conditioning and updating.}, 3250 author = {Thomas Augustin and Frank P. A. Coolen}, 3251 doi = {10.1016/j.jspi.2003.07.003}, 3252 journal = {Journal of Statistical Planning and Inference}, 3253 keywords = {A(n); Capacities; Conditioning; Consistency; Imprecise probabilities; Interval probability; Low structure inference; Non- parametrics; Predictive inference; Updating}, 3254 localfile = {article/Augustin-Coolen-2004.pdf}, 3255 number = {2}, 3256 pages = {251–272}, 3257 title = {Nonparametric predictive inference and interval probability}, 3258 volume = {124}, 3259 year = {2004} 3260 } 3261 3262 @techreport{Walley-1981, 3263 annote = {only the part on 2-monotonicity}, 3264 author = {Peter Walley}, 3265 institution = {Department of statistics, University of Warwick}, 3266 title = {Coherent lower (and upper) probabilities}, 3267 year = {1981} 3268 } 3269 3270 @article{Nash-1951, 3271 annote = {ook op papier}, 3272 author = {John Nash}, 3273 journal = {The Annals of Mathematics}, 3274 localfile = {article/Nash-1951.pdf}, 3275 number = {2}, 3276 pages = {286–295}, 3277 title = {Non-cooperative games}, 3278 url = {http://www.jstor.org/stable/1969529}, 3279 volume = {54}, 3280 year = {1951} 3281 } 3282 3283 @mastersthesis{Walter-2006, 3284 author = {Gero Walter}, 3285 localfile = {mastersthesis/Walter-2006.pdf}, 3286 school = {Ludwig-Maximilians-Universität München}, 3287 title = {Robuste Bayes-Regression mit Mengen von Prioris – Ein Beitrag zur Statistik unter komplexer Unsicherheit}, 3288 url = {http://www.stat.uni-muenchen.de/~thomas/team/diplomathesis_GeroWalter.pdf}, 3289 year = {2006} 3290 } 3291 3292 @article{Trump-Prautzsch-1996, 3293 abstract = {In this paper we present fast algorithms to raise the degree 3294 n of a simplicial Bézier representation of degree n to arbitrarily high degree. 3295 Each Bézier point of some (n + r)th degree representation can be computed in a 3296 simplicial recursive scheme of depth n. In the case of curves the recurrence 3297 relation reveals that the (n + r)th degree Bézier polygon can also be obtained 3298 by inserting r knots into some nth degree spline which provides a very fast 3299 algorithm. Furthermore, a short new proof is given for the fact that the Bézier 3300 nets of a multivariate polynomial converge to the polynomial under repeated 3301 degree elevation.}, 3302 author = {Wilfried Trump and Hartmut Prautzsch}, 3303 doi = {10.1016/0167-8396(95)00031-3}, 3304 journal = {Computer Aided Geometric Design}, 3305 keywords = {Bézier curves; Bézier simplices; Bézier triangles; b-splines; convergence; elevation; knot insertion; pyramidal schemes; repeated degree; simplicial recursions}, 3306 localfile = {article/Trump-Prautzsch-1996.pdf}, 3307 number = {5}, 3308 pages = {387–398}, 3309 publisher = {Elsevier}, 3310 title = {Arbitrarily high degree elevation of Bézier representations}, 3311 volume = {13}, 3312 year = {1996} 3313 } 3314 3315 @article{Miranda-Zaffalon-2011, 3316 abstract = {We detail the relationship between sets of desirable gambles 3317 and conditional lower previsions. The former is one the most general models of 3318 uncertainty. The latter corresponds to Walley’s celebrated theory of imprecise 3319 probability. We consider two avenues: when a collection of conditional lower 3320 previsions is derived from a set of desirable gambles, and its converse. In 3321 either case, we relate the properties of the derived model with those of the 3322 originating one. Our results constitute basic tools to move from one formalism 3323 to the other, and thus to take advantage of work done in the two fronts.}, 3324 author = {Enrique Miranda and Marco Zaffalon}, 3325 doi = {10.1007/s10472-011-9231-4}, 3326 issn = {1012-2443}, 3327 issue = {3}, 3328 journal = {Annals of Mathematics and Artificial Intelligence}, 3329 keyword = {Computer Science}, 3330 keywords = {coherence; equal expressivity; lower and upper previsions; mathematics subject classifications; natural extension; sets of desirable gambles}, 3331 localfile = {article/Miranda-Zaffalon-2011.pdf}, 3332 pages = {251–309}, 3333 publisher = {Springer Netherlands}, 3334 title = {Notes on desirability and conditional lower previsions}, 3335 volume = {60}, 3336 year = {2011} 3337 } 3338 3339 @proceedings{WWW-2002, 3340 booktitle = {Proceedings of the Eleventh International World Wide Web Conference}, 3341 title = {Proceedings of the Eleventh International World Wide Web Conference}, 3342 year = {2002} 3343 } 3344 3345 @inproceedings{Couso-Moral-2009-ISIPTA, 3346 address = {Durham, United Kingdom}, 3347 author = {Inés Couso and Serafín Moral}, 3348 booktitle = {ISIPTA '09: Proceedings of the Sixth International Symposium on Imprecise Probabilities: Theories and Applications}, 3349 editor = {Thomas Augustin and Frank P. A. Coolen and Serafin Moral and Matthias C. M. Troffaes}, 3350 organization = {SIPTA}, 3351 pages = {99–108}, 3352 title = {Sets of desirable gambles and credal sets}, 3353 url = {http://www.sipta.org/isipta09/proceedings/063.html}, 3354 year = {2009} 3355 } 3356 3357 @article{Mantel-1976-tails, 3358 author = {Nathan Mantel}, 3359 journal = {The American Statistician}, 3360 localfile = {article/Mantel-1976-tails.pdf}, 3361 number = {1}, 3362 pages = {14–17}, 3363 title = {Tails of Distributions}, 3364 url = {http://www.jstor.org/stable/2682880}, 3365 volume = {30}, 3366 year = {1976} 3367 } 3368 3369 @book{Jaynes-2003, 3370 author = {E. T. Jaynes}, 3371 editor = {J. Larry Bretthorst}, 3372 publisher = {Cambridge University Press}, 3373 title = {Probability Theory: The Logic of Science}, 3374 year = {2003} 3375 } 3376 3377 @incollection{Shapley-1964-twoperson, 3378 author = {Lloyd S. Shapley}, 3379 booktitle = {Advances in game theory}, 3380 editor = {D. Dresher and L. S. Shapley and A. W. Tucker}, 3381 publisher = {Princeton University Press}, 3382 title = {Some topics in two-person games}, 3383 year = {1964} 3384 } 3385 3386 @article{Shannon-1948, 3387 annote = {ook op papier}, 3388 author = {Claude E. Shannon}, 3389 journal = {The Bell System Technical Journal}, 3390 localfile = {article/Shannon-1948.pdf}, 3391 pages = {379–423,623–656}, 3392 title = {A Mathematical Theory of Communication}, 3393 url = {http://cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf}, 3394 volume = {27}, 3395 year = {1948} 3396 } 3397 3398 @inproceedings{Schervish-Seidenfeld-Kadane-1999-incoherence, 3399 abstract = {We introduce two indices for the degree of incoherence in a 3400 set of lower and upper previsions: maximizing the rate of loss the incoherent 3401 Bookie experiences in a Dutch Book, or maximizing the rate of profit the Gambler 3402 achieves who makes Dutch Book against the incoherent Bookie. We report how 3403 efficient bookmaking is achieved against these two indices in the case of 3404 incoherent previsions for events on a finite partition, and for incoherent 3405 previsions that include also a simple random variable. We relate the 3406 epsilon-contamination model to efficient bookmaking in the case of the rate of 3407 profit.}, 3408 address = {Ghent, Belgium}, 3409 author = {Mark J. Schervish and Teddy Seidenfeld and Joseph B. Kadane}, 3410 booktitle = {ISIPTA '99: Proceedings of the First International Symposium on Imprecise probabilities and Their Applications}, 3411 editor = {Gert {De Cooman} and Fabio Gagliardi Cozman and Serafin Moral and Peter Walley}, 3412 keywords = {Dutch Book; coherence; epsilon-contamination mod}, 3413 pages = {319–323}, 3414 title = {How Sets of Coherent Probabilities may Serve as Models for Degrees of Incoherence}, 3415 url = {http://decsai.ugr.es/~smc/isipta99/proc/072.html}, 3416 year = {1999} 3417 } 3418 3419 @phdthesis{Jaeger-1995, 3420 address = {Saarbrücken}, 3421 author = {Manfred Jaeger}, 3422 school = {Universität des Saarlandes}, 3423 title = {Default Reasoning about Probabilities}, 3424 year = {1995} 3425 } 3426 3427 @book{Cowell-etal-2003-expert, 3428 author = {R. G. Cowell and A. Philip Dawid and Steffen L. Lauritzen and D. J. Spiegelhalter}, 3429 isbn = {978-0-387-98767-5}, 3430 publisher = {Springer}, 3431 series = {Information Science and Statistics}, 3432 title = {Probabilistic Networks and Expert Systems}, 3433 year = {2003} 3434 } 3435 3436 @article{Kunreuther-et-al-2002, 3437 abstract = {This paper reviews the state of the art of research on 3438 individual decision-making in high-stakes, low-probability settings. A central 3439 theme is that resolving high-stakes decisions optimally poses a formidable 3440 challenge not only to naïve decision makers, but also to users of more 3441 sophisticated tools, such as decision analysis. Such decisions are difficult to 3442 make because precise information about probabilities is not available, and the 3443 dynamics of the decision are complex. When faced with such problems, naïve 3444 decision-makers fall prey to a wide range of potentially harmful biases, such as 3445 failing to recognize a high-stakes problem, ignoring the information about 3446 probabilities that does exist, and responding to complexity by accepting the 3447 status quo. A proposed agenda for future research focuses on how the process and 3448 outcomes of high-stakes decision making might be improved.}, 3449 author = {Howard C. Kunreuther and Robert Meyer and Richard Zeckhauser and Paul Slovic and Barry Schwartz and Christian Schade and Mary Frances Luce and Steven Lippman and David H. Krantz and Barbara Kahn and Robin Hogarth}, 3450 doi = {10.1023/A:1020287225409}, 3451 journal = {Marketing Letters}, 3452 keywords = {decision biases; decision heuristics; decision making under certainty; high-stakes decisions; risky decision making}, 3453 localfile = {article/Kunreuther-et-al-2002.pdf}, 3454 number = {3}, 3455 pages = {259–268}, 3456 publisher = {Springer}, 3457 title = {High stakes decision making: Normative, descriptive and prescriptive considerations}, 3458 volume = {13}, 3459 year = {2002} 3460 } 3461 3462 @article{McKinney-1962, 3463 author = {Richard L. McKinney}, 3464 doi = {10.1090/S0002-9947-1962-0147879-X}, 3465 journal = {Transactions of the American Mathematical Society}, 3466 localfile = {article/McKinney-1962.pdf}, 3467 pages = {131–148}, 3468 title = {Positive bases for linear spaces}, 3469 url = {http://www.ams.org/journals/tran/1962-103-01/S0002-9947-1962-0147879-X/S0002-99 3470 47-1962-0147879-X.pdf}, 3471 volume = {103}, 3472 year = {1962} 3473 } 3474 3475 @article{Hartfiel-1991, 3476 abstract = {Let T be a non-empty subset of n x n stochastic matrices. 3477 Define T2={A1A2 | A1,A2∈T}, T3= {A1A2A3 | A1,A2,A3∈T}, ⋯. The sequence T1,T2,⋯ 3478 is called a Markov set-chain. An important problem in this area is to determine 3479 when such a set-chain converges. This paper gives a notion of a sequential 3480 limiting set and shows how it can be used to obtain a result on set-chain 3481 convergence.}, 3482 author = {Darald J. Hartfiel}, 3483 issn = {0021-9002}, 3484 journal = {Journal of Applied Probability}, 3485 localfile = {article/Hartfiel-1991.pdf}, 3486 number = {4}, 3487 pages = {910–913}, 3488 publisher = {Applied Probability Trust}, 3489 title = {Sequential limits in Markov set-chains}, 3490 url = {http://www.jstor.org/stable/3214695}, 3491 volume = {28}, 3492 year = {1991} 3493 } 3494 3495 @article{Coolen-Augustin-2009-IDM-alternative, 3496 abstract = {Nonparametric predictive inference (NPI) is a general 3497 methodology to learn from data in the absence of prior knowledge and without 3498 adding unjustified assumptions. This paper develops NPI for multinomial data 3499 when the total number of possible categories for the data is known. We present 3500 the upper and lower probabilities for events involving the next observation and 3501 several of their properties. We also comment on differences between this NPI 3502 approach and corresponding inferences based on Walley's Imprecise Dirichlet 3503 Model.}, 3504 annote = {Special Section on The Imprecise Dirichlet Model and Special Section on Bayesian Robustness (Issues in Imprecise Probability)}, 3505 author = {Frank P. A. Coolen and Thomas Augustin}, 3506 doi = {10.1016/j.ijar.2008.03.011}, 3507 issn = {0888-613X}, 3508 journal = {International Journal of Approximate Reasoning}, 3509 keywords = {Circular A(n); Imprecise Dirichlet Model; Imprecise probabilities; Interval probability; Lower and upper probabilities; Multinomial data; Nonparametric predictive inference; Rule of succession}, 3510 localfile = {article/Coolen-Augustin-2008-IDM-alternative.pdf}, 3511 number = {2}, 3512 pages = {217–230}, 3513 publisher = {Elsevier}, 3514 title = {A nonparametric predictive alternative to the Imprecise Dirichlet Model: the case of a known number of categories}, 3515 volume = {50}, 3516 year = {2009} 3517 } 3518 3519 @proceedings{ISIPTA-1999, 3520 address = {Ghent, Belgium}, 3521 booktitle = {ISIPTA '99: Proceedings of the First International Symposium on Imprecise probabilities and Their Applications}, 3522 editor = {Gert {De Cooman} and Fabio Gagliardi Cozman and Serafin Moral and Peter Walley}, 3523 title = {ISIPTA '99: Proceedings of the First International Symposium on Imprecise Probabilities and Their Applications}, 3524 year = {1999} 3525 } 3526 3527 @article{Koopman-1940-axioms, 3528 author = {B. O. Koopman}, 3529 issn = {0003-486X}, 3530 journal = {The Annals of Mathematics}, 3531 localfile = {article/Koopman-1940-axioms.pdf}, 3532 number = {2}, 3533 pages = {269–292}, 3534 title = {The axioms and algebra of intuitive probability}, 3535 url = {http://www.jstor.org/stable/1969003}, 3536 volume = {41}, 3537 year = {1940} 3538 } 3539 3540 @misc{Manski-2003, 3541 author = {Charles F. Manski}, 3542 title = {Partial identification of probability distributions}, 3543 year = {2003} 3544 } 3545 3546 @article{Inuiguchi-2006, 3547 author = {Masahiro Inuiguchi}, 3548 journal = {Kybernetika}, 3549 keywords = {bender; fuzzy linear programming; necessity measure; oblique fuzzy vector; s}, 3550 localfile = {article/Inuiguchi-2006.pdf}, 3551 number = {4}, 3552 pages = {441–452}, 3553 publisher = {THE ACADEMY OF SCIENCES OF THE CZECH REPUBLIC}, 3554 title = {A necessity measure optimization approach to linear programming problems with oblique fuzzy vectors}, 3555 url = {http://hdl.handle.net/10338.dmlcz/135726}, 3556 volume = {42}, 3557 year = {2006} 3558 } 3559 3560 @inproceedings{Fuller-Zimmermann-1992, 3561 author = {Robert Fullér and Hans-Jürgen Zimmermann}, 3562 booktitle = {Proceedings of 2nd International Workshop on Current Issues in Fuzzy Technologies}, 3563 title = {Approximate Reasoning for Solving Fuzzy Linear Programming Problems}, 3564 year = {1992} 3565 } 3566 3567 @article{Northrop-1936-prob-in-QM, 3568 author = {F. S. C. Northrop}, 3569 journal = {Philosophy of Science}, 3570 localfile = {article/Northrop-1936-prob-in-QM.pdf}, 3571 number = {2}, 3572 pages = {215–232}, 3573 title = {The Philosophical Significance of the Concept of Probability in Quantum Mechanics}, 3574 url = {http://www.jstor.org/stable/184348}, 3575 volume = {3}, 3576 year = {1936} 3577 } 3578 3579 @misc{Cozman-2003, 3580 author = {Fabio Gagliardi Cozman}, 3581 note = {slide printout}, 3582 title = {Graph-Theoretical Models for Multivariate Modeling with Imprecise Probabilities}, 3583 year = {2003} 3584 } 3585 3586 @article{Avis-Bremner-Seidel-1997, 3587 abstract = {A convex polytope P can be specified in two ways: as the 3588 convex hull of the vertex set V of P, or as the intersection of the set H of its 3589 facet-inducing halfspaces. The vertex enumeration problem is to compute V from 3590 H. The facet enumeration problem is to compute H from V. These two problems are 3591 essentially equivalent under point/hyperplane duality. They are among the 3592 central computational problems in the theory of polytopes. It is open whether 3593 they can be solved in time polynomial in |H| + |V| and the dimension. In this 3594 paper we consider the main known classes of algorithms for solving these 3595 problems. We argue that they all have at least one of two weaknesses: inability 3596 to deal well with "degeneracies", or, inability to control the sizes of 3597 intermediate results. We then introduce families of polytopes that exercise 3598 those weaknesses. Roughly speaking, fat-lattice or intricate polytopes cause 3599 algorithms with bad degeneracy handling to perform badly; dwarfed polytopes 3600 cause algorithms with bad intermediate size control to perform badly. We also 3601 present computational experience with trying to solve these problem on these 3602 hard polytopes, using various implementations of the main algorithms.}, 3603 annote = {ook op papier}, 3604 author = {David Avis and David Bremner and Raimund Seidel}, 3605 doi = {10.1016/S0925-7721(96)00023-5}, 3606 journal = {Computational Geometry}, 3607 keywords = {Convex hulls; Convex polytopes; Lattice complexity; Triangulation complexity; Vertex enumeration}, 3608 localfile = {article/Avis-Bremner-Seidel-1997.pdf}, 3609 pages = {265–301}, 3610 title = {How good are convex hull algorithms?}, 3611 volume = {7}, 3612 year = {1997} 3613 } 3614 3615 @article{OHara-OHara-1999, 3616 author = {K. O'Hara and J. O'Hara}, 3617 doi = {10.1046/j.1464-410x.1999.0830s1079.x}, 3618 issn = {1464-4096}, 3619 journal = {BJU international}, 3620 keywords = {Age Distribution; Circumcision; Coitus; Female; Humans; Interpersonal Relations; Male; Male: adverse effects; Male: psychology; Orgasm; Sexual Behavior; Sexual Partners; Sexual Partners: psychology}, 3621 localfile = {article/OHara-OHara-1999.pdf}, 3622 month = jan, 3623 number = {Supplement 1}, 3624 pages = {79–84}, 3625 pmid = {10349418}, 3626 title = {The effect of male circumcision on the sexual enjoyment of the female partner.}, 3627 volume = {83}, 3628 year = {1999} 3629 } 3630 3631 @article{Genest-MacKay-1986, 3632 author = {Christian Genest and Jock MacKay}, 3633 journal = {The American Statistician}, 3634 keywords = {Archimedean copulas; Fréchet bounds; Kendall's tau; fixed marginals; singular distributions}, 3635 localfile = {article/Genest-MacKay-1986.pdf}, 3636 number = {4}, 3637 pages = {280–283}, 3638 title = {The joy of copulas: bivariate distributions with uniform marginals}, 3639 url = {http://www.jstor.org/stable/2684602}, 3640 volume = {40}, 3641 year = {1986} 3642 } 3643 3644 @article{Rudolph-1996-duality, 3645 abstract = {Using elementary module theory, an intrinsic definition of 3646 the dual (or adjoint) of a generalized time-varying linear system is given. With 3647 this, the duality of controllability and observability is recovered from their 3648 intrinsic module theoretical definitions. The duality of state feedback and 3649 output injection is discussed both in the static case and for its quasistatic 3650 generalization. Related Brunovsky type canonical forms are derived in the 3651 quasistatic case. The corresponding controllability indices and their duals the 3652 observability indices are defined intrinsically.}, 3653 author = {J. Rudolph}, 3654 doi = {10.1016/0024-3795(94)00222-3}, 3655 issn = {0024-3795}, 3656 journal = {Linear Algebra and its Applications}, 3657 localfile = {article/Rudolph-1996-duality.pdf}, 3658 pages = {83–106}, 3659 title = {Duality in time-varying linear systems: a module theoretic approach}, 3660 volume = {245}, 3661 year = {1996} 3662 } 3663 3664 @article{Benavoli-et-al-2010, 3665 abstract = {We extend hidden Markov models for continuous variables 3666 taking into account imprecision in our knowledge about the probabilistic 3667 relationships involved. To achieve that, we consider sets of probabilities, also 3668 called coherent lower previsions. In addition to the general formulation, we 3669 study in detail a particular case of interest: linear-vacuous mixtures. We also 3670 show, in a practical case, that our extension outperforms the Kalman filter when 3671 modelling errors are present in the system.}, 3672 address = {Seattle, Washington}, 3673 annote = {ook op papier}, 3674 author = {Alessio Benavoli and Marco Zaffalon and Enrique Miranda}, 3675 journal = {IEEE Transactions on Automatic Control}, 3676 localfile = {article/Benavoli-et-al-2010.pdf}, 3677 organization = {IEEE}, 3678 pages = {1743–1750}, 3679 title = {A new robust approach to filtering based on coherent lower previsions}, 3680 year = {2009} 3681 } 3682 3683 @proceedings{IPMU-2002, 3684 booktitle = {Proceedings of the Ninth International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems: IPMU 2002}, 3685 title = {Proceedings of the Ninth International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems: IPMU 2002}, 3686 year = {2002} 3687 } 3688 3689 @article{Savage-1971, 3690 author = {Leonard J. Savage}, 3691 journal = {Journal of the American Statistical Association}, 3692 localfile = {article/Savage-1971.pdf}, 3693 number = {336}, 3694 pages = {783–801}, 3695 title = {Elicitation of personal probabilities and expectations}, 3696 url = {http://www.jstor.org/stable/2284229}, 3697 volume = {66}, 3698 year = {1971} 3699 } 3700 3701 @techreport{Minka-2001, 3702 author = {Thomas P. Minka}, 3703 title = {Bayesian linear regression}, 3704 year = {2001} 3705 } 3706 3707 @article{Lange-1995, 3708 author = {Kenneth Lange}, 3709 doi = {10.1007/BF01441156}, 3710 journal = {Genetica}, 3711 localfile = {article/Lange-1995.pdf}, 3712 number = {1}, 3713 pages = {107–117}, 3714 publisher = {Springer}, 3715 title = {Applications of the Dirichlet distribution to forensic match probabilities}, 3716 volume = {96}, 3717 year = {1995} 3718 } 3719 3720 @techreport{Miranda-2008-updating, 3721 annote = {ook op papier}, 3722 author = {Enrique Miranda}, 3723 institution = {Department of Statistics and Operations Research, Rey Juan Carlos University}, 3724 title = {Updating coherent previsions on finite spaces}, 3725 year = {2008} 3726 } 3727 3728 @article{Goodhardt-Ehrenberg-Chatfield-1984, 3729 abstract = {The Dirichlet is a stochastic model of purchase incidence 3730 and brand choice which parsimoniously integrates a wide range of already 3731 well-established empirical regularities.}, 3732 annote = {ook op papier}, 3733 author = {G. J. Goodhardt and A. S. C. Ehrenberg and C. Chatfield}, 3734 journal = {Journal of the Royal Statistical Society. Series A (General)}, 3735 localfile = {article/Goodhardt-Ehrenberg-Chatfield-1984.pdf}, 3736 number = {5}, 3737 pages = {621–655}, 3738 title = {The Dirichlet: a comprehensive model of buying behaviour}, 3739 url = {http://www.jstor.org/stable/2981696}, 3740 volume = {147}, 3741 year = {1984} 3742 } 3743 3744 @article{DeCooman-Troffaes-Miranda-2005, 3745 abstract = {We study n-monotone lower previsions, which constitute a 3746 generalisation of n-monotone lower probabilities. We investigate their relation 3747 with the concepts of coherence and natural extension in the behavioural theory 3748 of imprecise probabilities, and improve along the way upon a number of results 3749 from the literature.}, 3750 author = {Gert {De Cooman} and Matthias C. M. Troffaes and Enrique Miranda}, 3751 journal = {Journal of Intelligent and Fuzzy Systems}, 3752 keywords = {Choquet integral; coherence; comonotone additivity; n-monotonicity; natural extension}, 3753 localfile = {article/DeCooman-Troffaes-Miranda-2005-Kerre.pdf}, 3754 number = {4}, 3755 pages = {253–263}, 3756 publisher = {IOS Press}, 3757 title = {n-Monotone lower previsions and lower integrals}, 3758 url = {http://iospress.metapress.com/content/22bh7djyjk86a55h}, 3759 volume = {16}, 3760 year = {2005} 3761 } 3762 3763 @book{Geisser-1993, 3764 author = {Seymour Geisser}, 3765 number = {55}, 3766 publisher = {Chapman \& Hall}, 3767 series = {Monographs on Statistics and Applied Probability}, 3768 title = {Predictive Inference: An Introduction}, 3769 year = {1993} 3770 } 3771 3772 @inproceedings{DeCooman-Quaeghebeur-2010-IPMU, 3773 address = {Berlin}, 3774 author = {Gert {De Cooman} and Erik Quaeghebeur}, 3775 booktitle = {Communications in Computer and Information Science}, 3776 doi = {10.1007/978-3-642-14055-6_7}, 3777 editor = {Eyke Hüllermeier and Rudolf Kruse and Frank Hoffmann}, 3778 isbn = {978-3-64214054-9}, 3779 issn = {1865-0929}, 3780 pages = {60–69}, 3781 publisher = {Springer}, 3782 title = {Infinite exchangeability for sets of desirable gambles}, 3783 volume = {80}, 3784 year = {2010} 3785 } 3786 3787 @article{Zaffalon-DeCooman-2005-editorial, 3788 annote = {reprint}, 3789 author = {Marco Zaffalon and Gert {De Cooman}}, 3790 doi = {10.1007/s10472-005-9009-7}, 3791 journal = {Annals of Mathematics and Artificial Intelligence}, 3792 pages = {1–4}, 3793 title = {Editorial: Imprecise probability perspectives on artificial intelligence}, 3794 volume = {45}, 3795 year = {2005} 3796 } 3797 3798 @book{Schneier-1996-crypto, 3799 annote = {stukken uit H5,6 op papier}, 3800 author = {Bruce Schneier}, 3801 publisher = {John Wiley \& Sons}, 3802 title = {Applied Cryptography}, 3803 url = {http://www.schneier.com/book-applied.html}, 3804 year = {1996} 3805 } 3806 3807 @inbook{DeFinetti-1972-notation, 3808 annote = {Translation of \cite{DeFinetti-1967} by Leonard J. Savage geringde kopie}, 3809 author = {Bruno de Finetti}, 3810 booktitle = {Probability, Induction and Statistics (The art of guessing)}, 3811 pages = {xviii–xxiv}, 3812 publisher = {John Wiley \& Sons}, 3813 title = {A Useful Notation}, 3814 year = {1972} 3815 } 3816 3817 @article{Harsanyi-1982-rejoinder, 3818 annote = {ook op papier}, 3819 author = {John C. Harsanyi}, 3820 doi = {10.1287/mnsc.28.2.124a}, 3821 journal = {Management Science}, 3822 localfile = {article/Harsanyi-1982-rejoinder.pdf}, 3823 number = {2}, 3824 pages = {124–125}, 3825 publisher = {INFORMS}, 3826 title = {Rejoinder to professors Kadane and Larkey}, 3827 volume = {28}, 3828 year = {1982} 3829 } 3830 3831 @article{Mazaheri-Nasri-2007, 3832 author = {H. Mazaheri and M. Nasri}, 3833 journal = {International Mathematical Forum}, 3834 localfile = {article/Mazaheri-Nasri-2007.pdf}, 3835 number = {16}, 3836 pages = {747–751}, 3837 title = {Complemented Subspaces in the Normed Spaces}, 3838 url = {http://www.m-hikari.com/imf-password2007/13-16-2007/mazaheriIMF13-16-2007-3.pdf 3839 }, 3840 volume = {2}, 3841 year = {2007} 3842 } 3843 3844 @article{Hofbauer-Sigmund-2003, 3845 author = {Josef Hofbauer and Karl Sigmund}, 3846 journal = {Bulletin of the American Mathematical Society}, 3847 number = {4}, 3848 pages = {479–519}, 3849 title = {Evolutionary game dynamics}, 3850 volume = {40}, 3851 year = {2003} 3852 } 3853 3854 @article{Antonucci-etal-2009-milident, 3855 abstract = {Credal networks are imprecise probabilistic graphical models 3856 generalizing Bayesian networks to convex sets of probability mass functions. 3857 This makes credal networks particularly suited to model expert knowledge under 3858 very general conditions, including states of qualitative and incomplete 3859 knowledge. In this paper, we present a credal network for risk evaluation in 3860 case of intrusion of civil aircrafts into a restricted flight area. The 3861 different factors relevant for this evaluation, together with an independence 3862 structure over them, are initially identified. These factors are observed by 3863 sensors, whose reliabilities can be affected by variable external factors, and 3864 even by the behaviour of the intruder. A model of these observation processes, 3865 and the necessary fusion scheme for the information returned by the sensors 3866 measuring the same factor, are both completely embedded into the structure of 3867 the credal network. A pool of experts, facilitated in their task by specific 3868 techniques to convert qualitative judgements into imprecise probabilistic 3869 assessments, has made possible the quantification of the network. We show the 3870 capabilities of the proposed model by means of some preliminary tests referred 3871 to simulated scenarios. Overall, we can regard this application as a useful tool 3872 to support military experts in their decision, but also as a quite general 3873 imprecise-probability paradigm for information fusion.}, 3874 author = {Alessandro Antonucci and Ralph Brühlmann and Alberto Piatti and Marco Zaffalon}, 3875 doi = {10.1016/j.ijar.2009.01.005}, 3876 issn = {0888-613X}, 3877 journal = {International Journal of Approximate Reasoning}, 3878 keywords = {Credal networks; Information fusion; Sensor management; Tracking systems}, 3879 localfile = {article/Antonucci-etal-2009-milident.pdf}, 3880 number = {4}, 3881 pages = {666–679}, 3882 title = {Credal networks for military identification problems}, 3883 volume = {50}, 3884 year = {2009} 3885 } 3886 3887 @book{Boole-1854, 3888 author = {George Boole}, 3889 publisher = {Macmillan}, 3890 title = {The laws of thought}, 3891 url = {http://www.gutenberg.org/ebooks/15114}, 3892 year = {1854} 3893 } 3894 3895 @inproceedings{Miranda-DeCooman-Couso-2002, 3896 abstract = {We discuss how lower previsions induced by multi-valued 3897 mappings fit into the framework of the behavioural theory of imprecise 3898 probabilities, and show how the notions of coherence and natural extension from 3899 that theory can be used to prove and generalise existing results in an elegant 3900 and straightforward manner. This provides a clear example for their explanatory 3901 and unifying power.}, 3902 annote = {uitgebreide versie, ook op papier}, 3903 author = {Enrique Miranda and Gert {De Cooman} and Inés Couso}, 3904 booktitle = {Proceedings of the Ninth International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems: IPMU 2002}, 3905 keywords = {coherence; conditioning; evidence theory}, 3906 title = {Lower previsions induced by multi-valued mappings}, 3907 year = {2002} 3908 } 3909 3910 @book{Ziegler-1995, 3911 author = {Günter M. Ziegler}, 3912 publisher = {Springer}, 3913 title = {Lectures on Polytopes}, 3914 year = {1995} 3915 } 3916 3917 @article{Bildikar-Patil-1968, 3918 abstract = {Let \mathbf{x} and \mathbf{$\theta$} denote s-dimensional 3919 column vectors. The components x\_1, x\_2,⋯ x\_s of \mathbf{x} are random 3920 variables jointly following an s-variate distribution and components 3921 $\theta$\_1, $\theta$\_2,⋯, $\theta$\_s of \mathbf{$\theta$} are real numbers. 3922 The random vector \mathbf{x} is said to follow an s-variate Exponential-type 3923 distribution with the parameter vector (pv) \mathbf{$\theta$}, if its 3924 probability function (pf) is given by \begin{equation*}\tag{1.1} f(\mathbf{x}, 3925 \mathbf{$\theta$}) = h(\mathbf{x}) \exp {\mathbf{x'$\theta$} - 3926 q(\mathbf{$\theta$})},\end{equation*} \mathbf{x} \varepsilon R\_s and 3927 \mathbf{$\theta$} \varepsilon (\mathbf{a}, \mathbf{b}) \subset R\_s. R\_s 3928 denotes the s-dimensional Euclidean space. The s-dimensional open interval 3929 (\mathbf{a}, \mathbf{b}) may or may not be finite. h(\mathbf{x}) is a function 3930 of \mathbf{x}, independent of \mathbf{$\theta$}, and q(\mathbf{$\theta$}) is a 3931 bounded analytic function of $\theta$\_1, $\theta$\_2,⋯ $\theta$\_s, independent 3932 of \mathbf{x}. We note that f(\mathbf{x}, \mathbf{$\theta$}), given by (1.1), 3933 defines the class of multivariate exponential-type distributions which includes 3934 distributions like multivariate normal, multinomial, multivariate negative 3935 binomial, multivariate logarithmic series, etc. This paper presents a 3936 theoretical study of the structural properties of the class of multivariate 3937 exponential-type distributions. For example, different distributions connected 3938 with a multivariate exponential-type distribution are derived. Statistical 3939 independence of the components x\_1, x\_2,⋯, x\_s is discussed. The problem of 3940 characterization of different distributions in the class is studied under 3941 suitable restrictions on the cumulants. A canonical representation of the 3942 characteristic function of an infinitely divisible (id), purely discrete random 3943 vector, whose moments of second order are all finite, is also obtained. 3944 $\phi$(\mathbf{t}), m(\mathbf{t}), k(\mathbf{t}) denote, throughout this paper, 3945 the characteristic function (ch. f.), the moment generating function (mgf), and 3946 the cumulant generating function (cgf), respectively, of a random vector 3947 \mathbf{x}. The components t\_i of the s-dimensional column vector \mathbf{t} 3948 are all real.}, 3949 annote = {ook op papier}, 3950 author = {Sheela Bildikar and G. P. Patil}, 3951 doi = {10.1214/aoms}, 3952 journal = {The Annals of Mathematical Statistics}, 3953 localfile = {article/Bildikar-Patil-1968.pdf}, 3954 number = {4}, 3955 pages = {1316–1326}, 3956 publisher = {Institute of Mathematical Statistics}, 3957 title = {Multivariate exponential-type distributions}, 3958 volume = {39}, 3959 year = {1968} 3960 } 3961 3962 @book{Laplace-1825-essai, 3963 address = {Paris}, 3964 author = {Pierre-Simon Laplace}, 3965 edition = {5}, 3966 publisher = {Bachelier}, 3967 title = {Essai philosophique sur les probabilités}, 3968 url = {http://books.google.com/books?id=Ovo3AAAAMAAJ}, 3969 year = {1825} 3970 } 3971 3972 @article{Koopman-1936, 3973 author = {B. O. Koopman}, 3974 journal = {Transactions of the American Mathematical Society}, 3975 localfile = {article/Koopman-1936.pdf}, 3976 number = {3}, 3977 pages = {399–409}, 3978 title = {On distributions admitting a sufficient statistic}, 3979 url = {http://www.ams.org/journals/tran/1936-039-03/S0002-9947-1936-1501854-3/S0002-99 3980 47-1936-1501854-3.pdf}, 3981 volume = {39}, 3982 year = {1936} 3983 } 3984 3985 @techreport{Nesterov-Palma-2000, 3986 annote = {geannoteerde reprint}, 3987 author = {Yu. Nesterov and André {De Palma}}, 3988 institution = {Center for Operations Research \& Econometrics, Université catholique de Louvain}, 3989 number = {2000/27}, 3990 title = {Stable dynamics in transportation systems}, 3991 type = {CORE discussion paper}, 3992 year = {2000} 3993 } 3994 3995 @proceedings{IPMU-2006, 3996 address = {Paris}, 3997 booktitle = {Proceedings of the Eleventh International Conference on Information Processing and Management of Uncertainty in Knowledge-based Systems}, 3998 title = {Information Processing and Management of Uncertainty in Knowledge-based Systems}, 3999 year = {2006} 4000 } 4001 4002 @inproceedings{Dash-Cooper-2002, 4003 author = {Denver Dash and Gregory F. Cooper}, 4004 booktitle = {Proceedings of the 19th International Conference on Machine Learning (ICML 2002)}, 4005 pages = {91–98}, 4006 title = {Exact model averaging with naive Bayesian classifiers}, 4007 year = {2002} 4008 } 4009 4010 @article{Fisher-1934, 4011 author = {R. A. Fisher}, 4012 doi = {10.1098/rspa.1934.0050}, 4013 journal = {Proceedings of the Royal Society of London, A}, 4014 localfile = {article/Fisher-1934.pdf}, 4015 pages = {285–307}, 4016 title = {Two new properties of mathematical likelihood}, 4017 volume = {144}, 4018 year = {1934} 4019 } 4020 4021 @article{Neumaier-2003-surprise, 4022 abstract = {This paper presents a new approach to fuzzy modeling based 4023 on the concept of surprise. The new concept is related to the traditional 4024 membership function by an antitone transformation. Advantages of the surprise 4025 approach include: 1. It has a consistent semantic interpretation. 2. It allows 4026 the joint use of quantitative and qualitative knowledge, using simple rules of 4027 logic. 3. It is a direct extension of (and allows combination with) the 4028 least-squares approach to reconciling conflicting approximate numerical data. 4. 4029 It is ideally suited to optimization under imprecise or conflicting goals, 4030 specified by a combination of soft and hard interval constraints. 5. It gives a 4031 straightforward approach to constructing families of functions consistent with 4032 fuzzy associative memories as used in fuzzy control, with tuning parameters 4033 (reflecting linguistic ambiguity) that can be adapted to available performance 4034 data.}, 4035 author = {Arnold Neumaier}, 4036 doi = {10.1016/S0165-0114(02)00248-8}, 4037 issn = {0165-0114}, 4038 journal = {Fuzzy Sets and Systems}, 4039 localfile = {article/Neumaier-2003-surprise.pdf}, 4040 number = {1}, 4041 pages = {21–38}, 4042 title = {Fuzzy modeling in terms of surprise}, 4043 volume = {135}, 4044 year = {2003} 4045 } 4046 4047 @article{Pelessoni-Vicig-2003-risk, 4048 abstract = {In this paper the theory of coherent imprecise previsions is 4049 applied to risk measurement. We introduce the notion of coherent risk measure 4050 defined on an arbitrary set of risks, showing that it can be considered a 4051 special case of coherent upper prevision. We also prove that our definition 4052 generalizes the notion of coherence for risk measures defined on a linear space 4053 of random numbers, given in literature. Consistency properties of Value-at-Risk 4054 (VaR), currently one of the most used risk measures, are investigated too, 4055 showing that it does not necessarily satisfy a weaker notion of consistency 4056 called 'avoiding sure loss'. We introduce sufficient conditions for VaR to avoid 4057 sure loss and to be coherent. Finally we discuss ways of modifying incoherent 4058 risk measures into coherent ones.}, 4059 author = {Renato Pelessoni and Paolo Vicig}, 4060 doi = {10.1142/S0218488503002156}, 4061 journal = {International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems}, 4062 keywords = {Imprecise prevision; Value-at-Risk; avoiding sure loss condition; coherent risk measure}, 4063 localfile = {article/Pelessoni-Vicig-2003-risk.pdf}, 4064 number = {4}, 4065 pages = {393–412}, 4066 title = {Imprecise previsions for risk measurement}, 4067 volume = {11}, 4068 year = {2003} 4069 } 4070 4071 @article{Dose-2007-gravity, 4072 author = {Volker Dose}, 4073 doi = {10.1088/0957-0233}, 4074 journal = {Measurement Science and Technology}, 4075 keywords = {gravitational constant; robust estimation}, 4076 localfile = {article/Dose-2007-gravity.pdf}, 4077 pages = {176–182}, 4078 title = {Bayesian estimate of the Newtonian constant of gravitation}, 4079 volume = {18}, 4080 year = {2007} 4081 } 4082 4083 @techreport{Coolen-Augustin-2006-cNPI4, 4084 author = {Frank P. A. Coolen and Thomas Augustin}, 4085 title = {Nonparametric predictive inference for multinomial data - Notes 4 (known number of categories, interval previsions for gambles, classification, and further comments)}, 4086 year = {2006} 4087 } 4088 4089 @article{Boumont-2002, 4090 author = {Jean-luc Doumont}, 4091 doi = {10.1109/TPC.2002.805164}, 4092 journal = {IEEE Transactions on Professional Communication}, 4093 localfile = {article/Doumont-2002.pdf}, 4094 month = dec, 4095 number = {4}, 4096 pages = {291–296}, 4097 title = {The three laws of professional communication}, 4098 volume = {45}, 4099 year = {2002} 4100 } 4101 4102 @book{Carnap-1952, 4103 address = {Chicago}, 4104 author = {Rudoplh Carnap}, 4105 publisher = {The University of Chicago Press}, 4106 title = {The Continuum of Inductive Methods}, 4107 year = {1952} 4108 } 4109 4110 @inproceedings{Brown-1951, 4111 author = {George W. Brown}, 4112 booktitle = {Activity analysis of production and allocation}, 4113 editor = {Tjalling C. Koopmans}, 4114 number = {13}, 4115 organization = {Cowles Commission for Research in Economics}, 4116 pages = {374–376}, 4117 series = {Cowles Commission Monographs}, 4118 title = {Iterative solution of games by fictitious play}, 4119 year = {1951} 4120 } 4121 4122 @article{Halpern-2010, 4123 abstract = {The relationship between Popper spaces (conditional 4124 probability spaces that satisfy some regularity conditions), lexicographic 4125 probability systems (LPS's), and nonstandard probability spaces (NPS's) is 4126 considered. If countable additivity is assumed, Popper spaces and a subclass of 4127 LPS's are equivalent; without the assumption of countable additivity, the 4128 equivalence no longer holds. If the state space is finite, LPS's are equivalent 4129 to NPS's. However, if the state space is infinite, NPS's are shown to be more 4130 general than LPS's.}, 4131 author = {Joseph Y. Halpern}, 4132 doi = {10.1016/j.geb.2009.03.013}, 4133 issn = {0899-8256}, 4134 journal = {Games and Economic Behavior}, 4135 localfile = {article/Halpern-2010.pdf}, 4136 number = {1}, 4137 pages = {155–179}, 4138 title = {Lexicographic probability, conditional probability, and nonstandard probability}, 4139 volume = {68}, 4140 year = {2010} 4141 } 4142 4143 @techreport{DeCooman-1991-margextconv, 4144 author = {Gert {De Cooman}}, 4145 title = {Marginal extension and convexity}, 4146 year = {2008} 4147 } 4148 4149 @misc{Lauritzen-2004b, 4150 annote = {Transparanten}, 4151 author = {Steffen L. Lauritzen}, 4152 title = {Exponential Families of Distributions}, 4153 year = {2004} 4154 } 4155 4156 @article{Fishburn-LaValle-1998, 4157 abstract = {The theory of subjective expected lexicographic utility 4158 brings together two classical developments in expected utility theory. The first 4159 is Hausner's theory of expected lexicographic utility in decision under risk. 4160 The second is a lottery-based theory of subjective expected utility in decision 4161 under uncertainty that was first axiomatized by Anscombe and Aumann. Our 4162 synthesis of the two produces representations of preference in decision 4163 underuncertainty in which utilities are finite-dimensional real vectors ordered 4164 lexicographicallyand subjective probabilities are real matrices. Axiomatizations 4165 of subjective expected lexicographic utility are described for finite and 4166 infinite sets of states. Procedures for assessing vector utilities and matrix 4167 probabilities are outlined.}, 4168 author = {Peter C. Fishburn and Irving H. LaValle}, 4169 doi = {10.1023/A:1018911830478}, 4170 issn = {0254-5330}, 4171 journal = {Annals of Operations Research}, 4172 localfile = {article/Fishburn-LaValle-1998.pdf}, 4173 pages = {183–206}, 4174 publisher = {Springer Netherlands}, 4175 title = {Subjective expected lexicographic utility: Axioms and assessment}, 4176 volume = {80}, 4177 year = {1998} 4178 } 4179 4180 @book{Schechter-1997-HAF, 4181 author = {Eric Schechter}, 4182 publisher = {Academic Press}, 4183 title = {Handbook of Analysis and Its Foundations}, 4184 year = {1997} 4185 } 4186 4187 @incollection{Seidenfeld-2000-reasonsforFA, 4188 author = {Teddy Seidenfeld}, 4189 booktitle = {Probability theory: philosophy, recent history and relations to science}, 4190 editor = {Vincent F. Hendricks and Stig Andur Pedersen and Klaus Frovin Jørgensen}, 4191 keywords = {improper regular conditional distributions}, 4192 publisher = {Kluwer Academic Publishers}, 4193 series = {Synthese Library}, 4194 title = {Remarks on the theory of conditional probability: some issues of finite versus countable additivity}, 4195 volume = {297}, 4196 year = {2001} 4197 } 4198 4199 @book{Ito-Kunisch-2008, 4200 author = {Kazufumi Ito and Karl Kunisch}, 4201 publisher = {SIAM}, 4202 title = {Lagrange Multiplier Approach to Variational Problems and Applications}, 4203 year = {2008} 4204 } 4205 4206 @article{Haldane-1945, 4207 author = {J. B. S. Haldane}, 4208 journal = {Biometrika}, 4209 localfile = {article/Haldane-1945.pdf}, 4210 number = {3}, 4211 pages = {222–225}, 4212 title = {On a method of estimating frequencies}, 4213 url = {http://www.jstor.org/stable/2332299}, 4214 volume = {33}, 4215 year = {1945} 4216 } 4217 4218 @book{Cramer-1946, 4219 author = {Harald Cramér}, 4220 publisher = {Princeton University Press}, 4221 title = {Mathematical methods of statistics}, 4222 year = {1946} 4223 } 4224 4225 @article{Halpern-Koller-2004, 4226 abstract = {Non-deductive reasoning systems are often representation 4227 dependent: representing the same situation in two di erent ways may cause such a 4228 system to return two different answers. Some have viewed this as a significant 4229 problem. For example, the principle of maximum entropy has been subjected to 4230 much criticism due to its representation dependence. There has, however, been 4231 almost no work investigating representation dependence. In this paper, we 4232 formalize this notion and show that it is not a problem specific to maximum 4233 entropy. In fact, we show that any representation-independent probabilistic 4234 inference procedure that ignores irrelevant information is essentially 4235 entailment, in a precise sense. Moreover, we show that representation 4236 independence is incompatible with even a weak default assumption of 4237 independence. We then show that invariance under a restricted class of 4238 representation changes can form a reasonable compromise between representation 4239 independence and other desiderata, and provide a construction of a family of 4240 inference procedures that provides such restricted representation independence, 4241 using relative entropy.}, 4242 annote = {ook op papier}, 4243 author = {Joseph Y. Halpern and Daphne Koller}, 4244 doi = {10.1613/jair.1292}, 4245 journal = {Journal of Artificial Intelligence Research}, 4246 localfile = {article/Halpern-Koller-2004.pdf}, 4247 pages = {319–356}, 4248 title = {Representation Dependence in Probabilistic Inference}, 4249 volume = {21}, 4250 year = {2004} 4251 } 4252 4253 @book{Bernardo-Smith-1994, 4254 author = {José M. Bernardo and Adrian F. M. Smith}, 4255 publisher = {Wiley}, 4256 series = {Wiley Series in Probability and Mathematical Statistics}, 4257 title = {Bayesian theory}, 4258 year = {1994} 4259 } 4260 4261 @manual{DeJongh-html, 4262 author = {Hans de Jong}, 4263 title = {Handleiding HTML}, 4264 url = {http://www.handleidinghtml.nl} 4265 } 4266 4267 @proceedings{WWW-2000, 4268 booktitle = {Proceedings of the Ninth International World Wide Web Conference}, 4269 title = {Proceedings of the Ninth International World Wide Web Conference}, 4270 year = {2000} 4271 } 4272 4273 @article{Oshime-1983, 4274 author = {Yorimasa Oshime}, 4275 journal = {Journal of mathematics of Kyoto university}, 4276 localfile = {article/Oshime-1983-Perron.pdf}, 4277 number = {4}, 4278 pages = {803–830}, 4279 title = {An extension of Morishima's nonlinear Perron-Frobenius theorem}, 4280 url = {http://projecteuclid.org/euclid.kjm/1250521436}, 4281 volume = {23}, 4282 year = {1983} 4283 } 4284 4285 @incollection{VanderGaag-Renooij-Coupe-2007, 4286 author = {Linda C. van der Gaag and Silja Renooij and Veerle M. H. Coupé}, 4287 booktitle = {Advances in Probabilistic Graphical Models}, 4288 doi = {10.1007/978-3-540-68996-6_5}, 4289 localfile = {inbook/VanderGaag-Renooij-Coupe-2007.pdf}, 4290 pages = {103–124}, 4291 publisher = {Springer}, 4292 title = {Sensitivity analysis of probabilistic networks}, 4293 volume = {124}, 4294 year = {2007} 4295 } 4296 4297 @article{Johnson-1967, 4298 abstract = {It is shown that the uniqueness of relationship between a 4299 regression function and a prior distribution, in Bates-Neyman type models, 4300 previously established for linear regressions and gamma prior distributions, is 4301 of much more general application.}, 4302 author = {Norman L. Johnson}, 4303 issn = {0162-1459}, 4304 journal = {Journal of the American Statistical Association}, 4305 localfile = {article/Johnson-1967.pdf}, 4306 number = {317}, 4307 pages = {288–289}, 4308 publisher = {American Statistical Association}, 4309 title = {Note on a uniqueness relation in certain accident proneness models}, 4310 url = {http://www.jstor.org/stable/2282931}, 4311 volume = {62}, 4312 year = {1967} 4313 } 4314 4315 @incollection{Shenoy-Shafer-2008-axioms, 4316 abstract = {In this paper, we describe an abstract framework and axioms 4317 under which exact local computation of marginals is possible. The primitive 4318 objects of the framework are variables and valuations. The primitive operators 4319 of the framework are combination and marginalization. These operate on 4320 valuations. We state three axioms for these operators and we derive the 4321 possibility of local computation from the axioms. Next, we describe a 4322 propagation scheme for computing marginals of a valuation when we have a 4323 factorization of the valuation on a hypertree. Finally we show how the problem 4324 of computing marginals of joint probability distributions and joint belief 4325 functions fits the general framework.}, 4326 author = {Prakash Shenoy and Glenn Shafer}, 4327 booktitle = {Classic Works of the Dempster-Shafer Theory of Belief Functions}, 4328 doi = {10.1007/978-3-540-44792-4_20}, 4329 editor = {Roland Yager and Liping Liu}, 4330 pages = {499–528}, 4331 publisher = {Springer}, 4332 series = {Studies in Fuzziness and Soft Computing}, 4333 title = {Axioms for Probability and Belief-Function Propagation}, 4334 volume = {219}, 4335 year = {2008} 4336 } 4337 4338 @article{Walley-DeCooman-2001, 4339 author = {Peter Walley and Gert {De Cooman}}, 4340 doi = {10.1016/S0020-0255(01)00090-1}, 4341 issn = {0020-0255}, 4342 journal = {Information Sciences}, 4343 keywords = {Imprecise probabilities; Linguistic information; Monotonic predicate; Plausibility ordering; Possibility distribution; Prototype theory; Vagueness}, 4344 localfile = {article/Walley-DeCooman-2001.pdf}, 4345 number = {1-4}, 4346 pages = {1–37}, 4347 title = {A behavioral model for linguistic uncertainty}, 4348 volume = {134}, 4349 year = {2001} 4350 } 4351 4352 @phdthesis{Quaeghebeur-2009-phd, 4353 author = {Erik Quaeghebeur}, 4354 school = {Ghent University}, 4355 title = {Learning from samples using coherent lower previsions}, 4356 year = {2009} 4357 } 4358 4359 @inproceedings{Quaeghebeur-DeCooman-Hermans-2011, 4360 author = {Erik Quaeghebeur and Gert {De Cooman} and Filip Hermans}, 4361 booktitle = {ISIPTA '11: Program and Abstracts}, 4362 keywords = {acceptability; desirability; favorability; indifference; preference}, 4363 pages = {29}, 4364 title = {Generalizing nonstrict and strict preference desirability}, 4365 url = {http://hdl.handle.net/1854/LU-1863955}, 4366 year = {2011} 4367 } 4368 4369 @article{Schervish-1989-forecaster, 4370 author = {Mark J. Schervish}, 4371 doi = {10.1214/aos}, 4372 journal = {The Annals of Statistics}, 4373 localfile = {article/Schervish-1989-forecaster.pdf}, 4374 number = {4}, 4375 pages = {1856–1879}, 4376 publisher = {Institute of Mathematical Statistics}, 4377 title = {A general method for comparing probability assessors}, 4378 url = {http://www.jstor.org/stable/2241668}, 4379 volume = {17}, 4380 year = {1989} 4381 } 4382 4383 @inproceedings{Nilim-ElGhaoui-2003-robust-Markov-NIPS, 4384 author = {Arnab Nilim and Laurent {El Ghaoui}}, 4385 booktitle = {NIPS}, 4386 editor = {Sebastian Thrun and Lawrence K Saul and Bernhard Schölkopf}, 4387 isbn = {0-262-20152-6}, 4388 publisher = {MIT Press}, 4389 title = {Robustness in Markov Decision Problems with Uncertain Transition Matrices}, 4390 year = {2003} 4391 } 4392 4393 @article{Hill-1968-An, 4394 abstract = {A Bayesian approach to inference about the percentiles and 4395 other characteristics of a finite population is proposed. The approach does not 4396 depend upon, though it need not exclude, the use of parametric models. Some 4397 related questions concerning the existence of exchangeable distributions are 4398 considered. It is shown that there are no countably additive exchangeable 4399 distributions on the space of observations which give ties probability 0 and for 4400 which a next observation is conditionally equally likely to fall in any of the 4401 open intervals between successive order statistics of a given sample.}, 4402 author = {Bruce M. Hill}, 4403 journal = {Journal of the American Statistical Association}, 4404 localfile = {article/Hill-1968-An.pdf}, 4405 number = {322}, 4406 pages = {677–691}, 4407 title = {Posterior distribution of percentiles: Bayes' theorem for sampling from a population}, 4408 url = {http://www.jstor.org/stable/2284038}, 4409 volume = {63}, 4410 year = {1968} 4411 } 4412 4413 @incollection{Wagner-2003-two-dogmas, 4414 annote = {op papier in Wagnerbundel}, 4415 author = {Carl G. Wagner}, 4416 booktitle = {The Epistemology of Keith Lehrer}, 4417 chapter = {9}, 4418 editor = {E. J. Olsson}, 4419 pages = {143–152}, 4420 publisher = {Kluwer Academic Publishers}, 4421 title = {Two dogmas of probabilism}, 4422 year = {2003} 4423 } 4424 4425 @book{Eckel-2000-C++V1, 4426 author = {Bruce Eckel}, 4427 edition = {2}, 4428 publisher = {Prentice Hall}, 4429 title = {Thinking in C++}, 4430 volume = {1}, 4431 year = {2000} 4432 } 4433 4434 @article{Walley-DeCooman-1999, 4435 abstract = {Possibility measures and conditional possibility measures 4436 are given a behavioural interpretation as marginal betting rates against events. 4437 Under this interpretation, possibility measures should satisfy two consistency 4438 criteria, known as ‘avoiding sure loss’ and ‘coherence’. We survey the rules 4439 that have been proposed for defining conditional possibilities and investigate 4440 which of them satisfy our consistency criteria in two situations of practical 4441 interest. Only two of these rules satisfy the criteria in both cases studied, 4442 and the conditional possibilities produced by these rules are highly 4443 uninformative. We introduce a new rule that is more informative and is also 4444 coherent in both cases.}, 4445 annote = {reprint}, 4446 author = {Peter Walley and Gert {De Cooman}}, 4447 doi = {10.1016/S0888-613X(99)00007-9}, 4448 journal = {International Journal of Approximate Reasoning}, 4449 keywords = {Dempster's rule; coherence; conditional possibility; imprecise probabilities; natural extension; possibility measure; possibility theory; upper probability}, 4450 localfile = {article/Walley-DeCooman-1999.pdf}, 4451 pages = {63–107}, 4452 title = {Coherence of rules for defining conditional possibility}, 4453 volume = {21}, 4454 year = {1999} 4455 } 4456 4457 @book{Bertsimas-Tsitsiklis-1997, 4458 author = {Dimitris Bertsimas and John N. Tsitsiklis}, 4459 isbn = {1-886529-19-1}, 4460 keywords = {Linear programming; integer programming; mathematical optimization}, 4461 publisher = {Athena Scientific}, 4462 title = {Introduction to linear optimization}, 4463 year = {1997} 4464 } 4465 4466 @book{Huygens-1920, 4467 author = {Christiaan Huygens}, 4468 publisher = {Martinus Nijhoff}, 4469 title = {Oevres complètes de Christiaan Huygens}, 4470 volume = {14}, 4471 year = {1920} 4472 } 4473 4474 @article{Zaffalon-Wesnes-Petrini-2003-dementia, 4475 abstract = {Dementia is a serious personal, medical and social problem. 4476 Recent research indicates early and accurate diagnoses as the key to effectively 4477 cope with it. No definitive cure is available but in some cases when the 4478 impairment is still mild the disease can be contained. This paper describes a 4479 diagnostic tool that jointly uses the naive credal classifier and the most 4480 widely used computerized system of cognitive tests in dementia research, the 4481 Cognitive Drug Research system. The naive credal classifier extends the discrete 4482 naive Bayes classifier to imprecise probabilities. The naive credal classifier 4483 models both prior ignorance and ignorance about the likelihood by sets of 4484 probability distributions. This is a new way to deal with small and incomplete 4485 datasets that departs significantly from most established classification 4486 methods. In the empirical study presented here, the naive credal classifier 4487 provides reliability and unmatched predictive performance. It delivers up to 4488 95\% correct predictions while being very robust with respect to the partial 4489 ignorance due to the largely incomplete data. The diagnostic tool also proves to 4490 be very effective in discriminating between Alzheimer's disease and dementia 4491 with Lewy bodies.}, 4492 author = {Marco Zaffalon and Keith Wesnes and Orlando Petrini}, 4493 doi = {10.1016/S0933-3657(03)00046-0}, 4494 journal = {Artificial Intelligence in Medicine}, 4495 keywords = {Cognitive tests; Credal classification; Dementia}, 4496 number = {1-2}, 4497 pages = {61–79}, 4498 title = {Reliable diagnoses of dementia by the naive credal classifier inferred from incomplete cognitive data}, 4499 volume = {29}, 4500 year = {2003} 4501 } 4502 4503 @article{Fishburn-1986, 4504 author = {Peter C. Fishburn}, 4505 doi = {10.1214/ss}, 4506 journal = {Statistical Science}, 4507 localfile = {article/Fishburn-1986.pdf}, 4508 number = {3}, 4509 pages = {335–345}, 4510 publisher = {Institute of Mathematical Statistics}, 4511 title = {The axioms of subjective probability}, 4512 volume = {1}, 4513 year = {1986} 4514 } 4515 4516 @book{Kolmogorov-1956, 4517 address = {New York}, 4518 annote = {English translation of Grundbegriffe der Wahrscheinlichkeit[s]rechnung, 1933}, 4519 author = {A. N. Kolmogorov}, 4520 edition = {Second}, 4521 editor = {Nathan Morisson}, 4522 publisher = {Chelsea publishing company}, 4523 title = {Foundations of the theory of probability}, 4524 year = {1956} 4525 } 4526 4527 @mastersthesis{Quaeghebeur-2002, 4528 abstract = {This text treats of the problem of predicting the flow of a 4529 river using past flow measurements, rainfall measurements and rainfall 4530 predictions. The objective is to generalize a forecasting method already used to 4531 predict daily consumption of electricity. The developed method will be compared 4532 to Hydromax, an existing riverflow forecasting model. The developed method 4533 simultaneously generates a series of consecutive flow predictions called a flow 4534 curve. This is done by combining separate forecasts for the mean, standard 4535 deviation and the normalized profile of the flow curve. Therefore, three 4536 separate forecasting models will be used, one for each of the aforementioned 4537 flow curve components. To understand the difficulties involved in riverflow 4538 forecasting we first take a look at the relevant hydrological concepts and the 4539 data used in constructing and testing the forecasting method. We will 4540 principally be interested in the prediction of floods, as these phenomena can 4541 have dire socioeconomic consequences if they take place without a timely 4542 warning. Some of the forecasting models will be based on mathematical techniques 4543 derived from the field of artificial neural networks. As an introduction we will 4544 shortly elaborate on this field before presenting a more profound study of the 4545 two derived techniques we will use. These are the so-called `self-organizing 4546 maps' and `radial basis function networks'. An essential part of the forecasting 4547 method are linear and nonlinear regression models. We shall take a look at these 4548 parameterized prediction models, the associated prediction errors and the 4549 parameter estimation involved in constructing them. Thus being well prepared, we 4550 will have at this stage a close look at the Hydromax model and explain the 4551 forecasting method we have developed. They will be compared in terms of the data 4552 needed and the hydrological knowledge involved. Finally, we will show how the 4553 developed method is used in practice. The obtained results will be compared with 4554 those obtained by Hydromax, and remarks will be made about possible 4555 improvements. We will conclude with showing that the developed method holds 4556 promise, but is not yet suitable for practical applications. Suggestions for 4557 further research are also included.}, 4558 author = {Erik Quaeghebeur}, 4559 localfile = {mastersthesis/Quaeghebeur-2002.pdf}, 4560 school = {Université catholique de Louvain}, 4561 title = {Analyse et prédiction de débit de rivières par des méthodes non linéaires}, 4562 url = {http://users.ugent.be/~equaeghe/content/EQ-2002-UCL-memoire-hyperlinked.pdf}, 4563 year = {2002} 4564 } 4565 4566 @article{Ghahramani-2001-HMM+BN-intro, 4567 abstract = {We provide a tutorial on learning and inference in hidden 4568 Markov models in the context of the recent literature on Bayesian networks. This 4569 perspective makes it possible to consider novel generalizations of hidden Markov 4570 models with multiple hidden state variables, multiscale representations, and 4571 mixed discrete and continuous variables. Although exact inference in these 4572 generalizations is usually intractable, one can use approximate inference 4573 algorithms such as Markov chain sampling and variational methods. We describe 4574 how such methods are applied to these generalized hidden Markov models. We 4575 conclude this review with a discussion of Bayesian methods for model selection 4576 in generalized HMMs.}, 4577 author = {Zoubin Ghahramani}, 4578 doi = {10.1142/S0218001401000836}, 4579 journal = {International Journal of Pattern Recognition and Artificial Intelligence}, 4580 keywords = {Dynamic Bayesian networks; hidden Markov models}, 4581 localfile = {article/Ghahramani-2001-HMM+BN-intro.pdf}, 4582 number = {1}, 4583 pages = {9–42}, 4584 title = {An introduction to hidden Markov models and Bayesian networks}, 4585 volume = {15}, 4586 year = {2001} 4587 } 4588 4589 @book{Abramowitz-Stegun-1972, 4590 editor = {Milton Abramowitz and Irene A Stegun}, 4591 publisher = {Dover}, 4592 title = {Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical tables}, 4593 url = {http://frameindex.htm}, 4594 year = {1972} 4595 } 4596 4597 @book{Fine-1973, 4598 address = {New York and London}, 4599 author = {Terrence L. Fine}, 4600 publisher = {Academic Press}, 4601 title = {Theories of Probability (An Examination of Foundations)}, 4602 year = {1973} 4603 } 4604 4605 @article{Basu-Pereira-1983a, 4606 abstract = {A Skibinsky (1970) characterization of the family of 4607 hypergeometric distributions is re-examined from the point of view of sufficient 4608 experiments and a number of other distributions similarly characterized.}, 4609 annote = {ook op papier}, 4610 author = {D. Basu and Carlos A. B. Pereira}, 4611 journal = {Sankhya Series A}, 4612 localfile = {article/Basu-Pereira-1983a.pdf}, 4613 number = {1}, 4614 pages = {99–104}, 4615 publisher = {Springer}, 4616 title = {A Note on Blackwell Sufficiency and a Skibinsky Characterization of Distributions}, 4617 url = {http://www.jstor.org/stable/25050417}, 4618 volume = {45}, 4619 year = {1983} 4620 } 4621 4622 @article{Fudenberg-Kreps-1993, 4623 abstract = {We study learning processes for finite strategic-form games, 4624 in which players use the history of past play to forecast play in the current 4625 period. In a generalization of fictitious play, we assume only that players 4626 asymptotically choose best responses to the historical frequencies of opponents′ 4627 past play. This implies that if the stage-game strategies converge, the limit is 4628 a Nash equilibrium. In the basic model, plays seems unlikely to converge to a 4629 mixed-strategy equilibrium, but such convergence is natural when the stage game 4630 is perturbed in the manner of Harsanyi′s purification theorem.}, 4631 annote = {geannoteerde kopie}, 4632 author = {Drew Fudenberg}, 4633 doi = {10.1006/game.1993.1021}, 4634 issn = {0899-8256}, 4635 journal = {Games and Economic Behavior}, 4636 localfile = {article/Fudenberg-Kreps-1993.pdf}, 4637 month = jul, 4638 number = {3}, 4639 pages = {320–367}, 4640 publisher = {MIT Press}, 4641 title = {Learning Mixed Equilibria}, 4642 volume = {5}, 4643 year = {1993} 4644 } 4645 4646 @article{Chateauneuf-Jaffray-1989, 4647 abstract = {Monotone capacities (on finite sets) of finite or infinite 4648 order (lower probabilities) are characterized by properties of their Möbius 4649 inverses. A necessary property of probabilities dominating a given capacity is 4650 demonstrated through the use of Gale's theorem for the transshipment problem. 4651 This property is shown to be also sufficient if and only if the capacity is 4652 monotone of infinite order. A characterization of dominating probabilities 4653 specific to capacities of order 2 is also proved.}, 4654 annote = {ook op papier}, 4655 author = {Alain Chateauneuf and Jean-Yves Jaffray}, 4656 doi = {10.1016/0165-4896(89)90056-5}, 4657 journal = {Mathematical Social Sciences}, 4658 keywords = {Decision theory; belief funct; lower probability}, 4659 localfile = {article/Chateauneuf-Jaffray-1989.pdf}, 4660 number = {3}, 4661 pages = {263–283}, 4662 publisher = {Elsevier}, 4663 title = {Some characterizations of lower probabilities and other monotone capacities through the use of Möbius inversion}, 4664 volume = {17}, 4665 year = {1989} 4666 } 4667 4668 @article{Wallner-2007-extremepoints, 4669 abstract = {Every coherent probability (= F-probability) \mathcal{F} on 4670 a finite sample space $Ømega$\_k with k elements defines a set of classical 4671 probabilities in accordance with the interval limits. This set, called 4672 "structure" of , is a convex polytope having dimension \leq k - 1. We prove that 4673 the maximal number of extreme points of structures is exactly k!.}, 4674 author = {Anton Wallner}, 4675 doi = {10.1016/j.ijar.2006.07.017}, 4676 journal = {International Journal of Approximate Reasoning}, 4677 keywords = {0/1-Matrix; Coherent probability; Core; Credal set; Extreme point; F-probability; Interval probability; Polyhedron; Polytope; Structure; Vertex}, 4678 localfile = {article/Wallner-2007-extremepoints.pdf}, 4679 number = {3}, 4680 pages = {339–357}, 4681 title = {Extreme points of coherent probabilities in finite spaces}, 4682 volume = {44}, 4683 year = {2007} 4684 } 4685 4686 @article{Quaeghebeur-DeCooman-2008-ELP-FSS, 4687 abstract = {We consider lower probabilities on finite possibility spaces 4688 as models for the uncertainty about the state. These generalizations of 4689 classical probabilities can have some interesting properties; for example: 4690 k-monotonicity, avoiding sure loss, coherence, permutation invariance. The sets 4691 formed by all the lower probabilities satisfying zero or more of these 4692 properties are convex. We show how the extreme points and rays of these sets – 4693 the extreme lower probabilities – can be calculated and we give an illustration 4694 of our results.}, 4695 author = {Erik Quaeghebeur and Gert {De Cooman}}, 4696 doi = {10.1016/j.fss.2007.11.020}, 4697 journal = {Fuzzy Sets and Systems}, 4698 keywords = {combinatorial problems; extreme points; imprecise probabilities; lower probabilities; non-additive measures}, 4699 localfile = {article/Quaeghebeur-DeCooman-2008-ELP-FSS.pdf}, 4700 month = sep, 4701 number = {16}, 4702 pages = {2163–2175}, 4703 publisher = {Elsevier}, 4704 title = {Extreme lower probabilities}, 4705 volume = {159}, 4706 year = {2008} 4707 } 4708 4709 @article{Heath-Sudderth-1976-exchangeability, 4710 abstract = {A simple proof is given for de Finetti's theorem that every 4711 sequence of exchangeable 0-1 random variables is a probability mixture of 4712 sequences of independent, identically distributed variables. The proof can 4713 easily be presented to seniors or first year graduate students of mathematical 4714 statistics and should aid them in understanding the relationship between the 4715 classical and the Bayesian point of view.}, 4716 author = {David Heath and William Sudderth}, 4717 journal = {The American Statistician}, 4718 localfile = {article/Heath-Sudderth-1976-exchangeability.pdf}, 4719 number = {4}, 4720 pages = {188–189}, 4721 title = {De Finetti's theorem on exchangeable variables}, 4722 url = {http://www.jstor.org/stable/2683760}, 4723 volume = {30}, 4724 year = {1976} 4725 } 4726 4727 @book{BangJensen-Gutin-2008-digraphs, 4728 author = {Jørgen Bang-Jensen and Gregory Gutin}, 4729 edition = {2}, 4730 publisher = {Springer}, 4731 title = {Digraphs: Theory, Algorithms and Applications}, 4732 url = {http://books.google.com/books?id=4UY-ucucWucC}, 4733 year = {2008} 4734 } 4735 4736 @incollection{Garloff-Graf-1999, 4737 author = {J. Garloff and B. Graf}, 4738 editor = {N. Munro}, 4739 pages = {339–352}, 4740 publisher = {The Institution of Electrical Engineers (IEE)}, 4741 title = {Solving strict polynomial inequalities by Bernstein expansion}, 4742 year = {1999} 4743 } 4744 4745 @unpublished{DeBoor-1995-BBForm, 4746 author = {C. de Boor}, 4747 keywords = {Bernstein polynomials}, 4748 title = {B-form basics}, 4749 year = {1995} 4750 } 4751 4752 @article{Zimmermann-1985, 4753 abstract = {Mathematical programming is one of the areas to which fuzzy 4754 set theory has been applied extensively. Primarily based on Bellman and Zadeh's 4755 model of decision in fuzzy environments, models have been suggested which allow 4756 flexibility in constraints and fuzziness in the objective function in 4757 traditional linear and nonlinear programming, in integer and fractional 4758 programming, and in dynamic programming. These models in turn have been used to 4759 offer computationally efficient approaches for solving vector maximum problems. 4760 This paper surveys major models and theories in this area and offers some 4761 indication on future developments which can be expected.}, 4762 author = {Hans-Jürgen Zimmermann}, 4763 doi = {10.1016/0020-0255(85)90025-8}, 4764 issn = {0020-0255}, 4765 journal = {Information Sciences}, 4766 number = {1-2}, 4767 pages = {29–58}, 4768 title = {Applications of fuzzy set theory to mathematical programming}, 4769 volume = {36}, 4770 year = {1985} 4771 } 4772 4773 @article{Wagner-1997-old+new, 4774 annote = {op papier in Wagnerbundel}, 4775 author = {Carl G. Wagner}, 4776 journal = {Philosophy of Science}, 4777 pages = {677–691}, 4778 title = {Old Evidence and New Explanation}, 4779 volume = {64}, 4780 year = {1997} 4781 } 4782 4783 @article{Friedman-1997, 4784 abstract = {The classification problem is considered in which an 4785 outputvariable y assumes discrete values with respectiveprobabilities that 4786 depend upon the simultaneous values of a set of input variablesx = 4787 {x\_1,....,x\_n}. At issue is how error in the estimates of theseprobabilities 4788 affects classification error when the estimates are used ina classification 4789 rule. These effects are seen to be somewhat counterintuitive in both their 4790 strength and nature. In particular the bias andvariance components of the 4791 estimation error combine to influenceclassification in a very different way than 4792 with squared error on theprobabilities themselves. Certain types of (very high) 4793 bias can becanceled by low variance to produce accurate classification. This 4794 candramatically mitigate the effect of the bias associated with some 4795 simpleestimators like “naive” Bayes, and the bias induced by 4796 thecurse-of-dimensionality on nearest-neighbor procedures. This helps explainwhy 4797 such simple methods are often competitive with and sometimes superiorto more 4798 sophisticated ones for classification, and why “bagging/aggregating” classifiers 4799 can often improveaccuracy. These results also suggest simple modifications to 4800 theseprocedures that can (sometimes dramatically) further improve 4801 theirclassification performance.}, 4802 author = {Jerome H. Friedman}, 4803 doi = {10.1023/A:1009778005914}, 4804 journal = {Data Mining and Knowledge Discovery}, 4805 keywords = {bagging; bias; classification; curse-of-dimensionality; naive Bayes; nearest-neighbors; variance}, 4806 localfile = {article/Friedman-1997.pdf}, 4807 number = {1}, 4808 pages = {55–77}, 4809 publisher = {Springer}, 4810 title = {On Bias, Variance, 0/1—Loss, and the Curse-of-Dimensionality}, 4811 volume = {1}, 4812 year = {1997} 4813 } 4814 4815 @phdthesis{Troffaes-2005, 4816 author = {Matthias C. M. Troffaes}, 4817 school = {Universiteit Gent – Ghent University}, 4818 title = {Optimaliteit, onzekerheid, en dynamisch programmeren met onderprevisies – Optimality, Uncertainty, and Dynamic Programming with Lower Previsions}, 4819 year = {2005} 4820 } 4821 4822 @proceedings{ISIPTA-2005, 4823 address = {Pittsburgh, Pennsylvania}, 4824 booktitle = {ISIPTA '05: Proceedings of the Fourth International Symposium on Imprecise Probabilities and Their Applications}, 4825 editor = {Fabio Gagliardi Cozman and Robert Nau and Teddy Seidenfeld}, 4826 organization = {SIPTA}, 4827 title = {ISIPTA '05: Proceedings of the Fourth International Symposium on Imprecise Probabilities and Their Applications}, 4828 year = {2005} 4829 } 4830 4831 @book{Rohn-2005, 4832 author = {Jiri Rohn}, 4833 title = {A Handbook of Results on Interval Linear Problems}, 4834 url = {http://uivtx.cs.cas.cz/~rohn/handbook}, 4835 year = {2005} 4836 } 4837 4838 @article{Wong-1998, 4839 abstract = {Generalized Dirichlet distribution has a more general 4840 covariance structure than Dirichlet distribution. This makes the generalized 4841 Dirichlet distribution to be more practical and useful. The concept of complete 4842 neutrality will be used to derive the general moment function for the 4843 generalized Dirichlet distribution, and then some properties of the generalized 4844 Dirichlet distribution will be established. Similar to the Dirichlet 4845 distribution, the generalized Dirichlet distribution will be shown to conjugate 4846 to multinominal sampling. Two experiments are designed for studying the 4847 differences between the Dirichlet and the generalized Dirichlet distributions in 4848 Bayesian analysis. A method for generating samples from a generalized Dirichlet 4849 in presented. When a prior distribution is either a Dirichlet or a generalized 4850 Dirichlet distribution, the way for constructing such a prior is discussed.}, 4851 annote = {ook op papier}, 4852 author = {Tzu-Tsung Wong}, 4853 doi = {10.1016/S0096-3003(97)10140-0}, 4854 journal = {Applied Mathematics and Computation}, 4855 keywords = {Bayesian analysis; Completely neutral; Conjugate; Generalized Dirichlet distribution; Prior construction}, 4856 localfile = {article/Wong-1998.pdf}, 4857 number = {2-3}, 4858 pages = {165–181}, 4859 publisher = {Elsevier}, 4860 title = {Generalized Dirichlet distribution in Bayesian analysis}, 4861 volume = {97}, 4862 year = {1998} 4863 } 4864 4865 @book{DeFinetti-1974/1975, 4866 author = {Bruno de Finetti}, 4867 publisher = {John Wiley \& Sons}, 4868 title = {Theory of Probability}, 4869 year = {1974-1975} 4870 } 4871 4872 @article{Hall-2006-sensitivity-indices, 4873 abstract = {An uncertainty-based sensitivity index represents the 4874 contribution that uncertainty in model input Xi makes to the uncertainty in 4875 model output Y. This paper addresses the situation where the uncertainties in 4876 the model inputs are expressed as closed convex sets of probability measures, a 4877 situation that exists when inputs are expressed as intervals or sets of 4878 intervals with no particular distribution specified over the intervals, or as 4879 probability distributions with interval-valued parameters. Three different 4880 approaches to measuring uncertainty, and hence uncertainty-based sensitivity, 4881 are explored. Variance-based sensitivity analysis (VBSA) estimates the 4882 contribution that each uncertain input, acting individually or in combination, 4883 makes to variance in the model output. The partial expected value of perfect 4884 information (partial EVPI), quantifies the (financial) value of learning the 4885 true numeric value of an input. For both of these sensitivity indices the 4886 generalization to closed convex sets of probability measures yields lower and 4887 upper sensitivity indices. Finally, the use of relative entropy as an 4888 uncertainty-based sensitivity index is introduced and extended to the imprecise 4889 setting, drawing upon recent work on entropy measures for imprecise 4890 information.}, 4891 author = {Jim W. Hall}, 4892 doi = {10.1016/j.ress.2005.11.042}, 4893 issn = {0951-8320}, 4894 journal = {Reliability Engineering \& System Safety}, 4895 keywords = {Coherent lower and upper probabilities; Entropy-based sensitivity indices; Generalized information theory; Partial expected value of perfect information; Variance-based sensitivity indices}, 4896 localfile = {article/Hall-2006-sensitivity-indices.pdf}, 4897 month = oct, 4898 number = {10-11}, 4899 pages = {1443–1451}, 4900 publisher = {Elsevier}, 4901 title = {Uncertainty-based sensitivity indices for imprecise probability distributions}, 4902 volume = {91}, 4903 year = {2006} 4904 } 4905 4906 @proceedings{CIPS-1951, 4907 address = {Paris}, 4908 booktitle = {Congrès international de philosophie des sciences. 4: Calcul des probabilités}, 4909 editor = {Raymond Bayer}, 4910 number = {1146}, 4911 publisher = {Hermann}, 4912 series = {Actualités scientifiques et industrielles}, 4913 title = {Congrès international de philosophie des sciences}, 4914 year = {1951} 4915 } 4916 4917 @book{Hume-1739, 4918 author = {David Hume}, 4919 edition = {Annotated}, 4920 editor = {David Fate Norton and Mary J. Norton}, 4921 publisher = {Oxford University Press}, 4922 series = {Oxford Philosophical Texts}, 4923 title = {A treatise of human nature}, 4924 year = {1739} 4925 } 4926 4927 @article{Rota-1964-moebius, 4928 author = {Gian-Carlo Rota}, 4929 doi = {10.1007/BF00531932}, 4930 journal = {Probability Theory and Related Fields}, 4931 localfile = {article/Rota-1964-moebius.pdf}, 4932 month = jan, 4933 number = {4}, 4934 pages = {340–368}, 4935 title = {On the foundations of combinatorial theory: I. Theory of Möbius functions}, 4936 volume = {2}, 4937 year = {1964} 4938 } 4939 4940 @article{Walley-Pelessoni-Vicig-2004, 4941 abstract = {We solve two fundamental problems of probabilistic 4942 reasoning: given finitely many conditional probability assessments, how to 4943 determine whether the assessments are mutually consistent, and how to determine 4944 what they imply about the conditional probabilities of other events? These 4945 problems were posed in 1854 by George Boole, who gave a partial solution using 4946 algebraic methods. The two problems are fundamental in applications of the 4947 Bayesian theory of probability; Bruno de Finetti solved the second problem for 4948 the special case of unconditional probability assessments in what he called ‘the 4949 fundamental theorem of probability’. We give examples to show that previous 4950 attempts to solve the two problems, using probabilistic logic and similar 4951 methods, can produce incorrect answers. Using ideas from the theory of imprecise 4952 probability, we show that the general problems have simple, direct solutions 4953 which can be implemented using linear programming algorithms. Unlike earlier 4954 proposals, our methods are formulated directly in terms of the assessments, 4955 without introducing unknown probabilities. Our methods work when any of the 4956 conditioning events may have probability zero, and they work when the 4957 assessments include imprecise (upper and lower) probabilities or previsions. The 4958 main methodological contribution of the paper is to provide general algorithms 4959 for making inferences from any finite collection of (possibly imprecise) 4960 conditional probabilities.}, 4961 author = {Peter Walley and Renato Pelessoni and Paolo Vicig}, 4962 doi = {10.1016/j.jspi.2003.09.005}, 4963 journal = {Journal of Statistical Planning and Inference}, 4964 keywords = {Avoiding uniform loss; Bayesian inference; Coherent probabilities; Fundamental theorem of probability; Imprecise probability; Lower probability; Natural extension; Probabilistic logic; Probabilistic reasoning}, 4965 localfile = {article/Walley-Pelessoni-Vicig-2004.pdf}, 4966 number = {1}, 4967 pages = {119–151}, 4968 title = {Direct algorithms for checking consistency and making inferences from conditional probability assessments}, 4969 volume = {126}, 4970 year = {2004} 4971 } 4972 4973 @article{Matheiss-Rubin-1980-vertexenum, 4974 abstract = {This paper surveys the literature on methods for finding all 4975 vertices of convex polytopes, contrasting the main features of each method and 4976 providing computational results for representative methods.}, 4977 annote = {ook op papier}, 4978 author = {T. H. Matheiss and David S. Rubin}, 4979 issn = {0364-765X}, 4980 journal = {Mathematics of Operations Research}, 4981 localfile = {article/Matheiss-Rubin-1980.pdf}, 4982 number = {2}, 4983 pages = {167–185}, 4984 title = {A survey and comparison of methods for finding all vertices of convex polyhedral sets}, 4985 url = {http://www.jstor.org/stable/3689148}, 4986 volume = {5}, 4987 year = {1980} 4988 } 4989 4990 @article{Friedman-2004, 4991 annote = {geannoteerde kopie}, 4992 author = {Nir Friedman}, 4993 doi = {10.1126/science.1094068}, 4994 journal = {Science}, 4995 localfile = {article/Friedman-2004.pdf}, 4996 number = {5659}, 4997 pages = {799–805}, 4998 publisher = {American Association for the Advancement of Science}, 4999 title = {Inferring cellular networks using probabilistic graphical models}, 5000 volume = {303}, 5001 year = {2004} 5002 } 5003 5004 @article{Bremner-Fukuda-Marzetta-1998-pd, 5005 author = {David Bremner and Komei Fukuda and Ambros Marzetta}, 5006 doi = {10.1007/PL00009389}, 5007 journal = {Discrete \& Computational Geometry}, 5008 pages = {333–357}, 5009 title = {Primal-Dual Methods for Vertex and Facet Enumeration}, 5010 url = {http://www.cs.unb.ca/profs/bremner/pd}, 5011 volume = {20}, 5012 year = {1998} 5013 } 5014 5015 @proceedings{CIM-1928, 5016 address = {Bologna}, 5017 booktitle = {Atti del congresso internationale dei matematici}, 5018 publisher = {N. Zanichelli}, 5019 title = {Atti del congresso internationale dei matematici}, 5020 year = {1928} 5021 } 5022 5023 @article{Goldstein-1983, 5024 abstract = {We prove that the result EX = E(E(X|Y)) is true, for bounded 5025 X, when the usual concept of conditional expectation or prevision is replaced by 5026 an alternative definition reflecting an individual's actual beliefs concerning X 5027 after observing Y. We discuss the importance of this result to subjectivist 5028 theory.}, 5029 author = {Michael Goldstein}, 5030 issn = {0162-1459}, 5031 journal = {Journal of the American Statistical Association}, 5032 keywords = {coherence}, 5033 localfile = {article/Goldstein-1983.pdf}, 5034 month = dec, 5035 number = {384}, 5036 pages = {817–819}, 5037 publisher = {American Statistical Association}, 5038 title = {The prevision of a prevision}, 5039 url = {http://www.jstor.org/stable/2288190}, 5040 volume = {78}, 5041 year = {1983} 5042 } 5043 5044 @article{Sarukkai-2000-link-prediction, 5045 abstract = {The enormous growth in the number of documents in the World 5046 Wide Web increases the need for improved link navigation and path analysis 5047 models. Link prediction and path analysis are important problems with a wide 5048 range of applications ranging from personalization to Web server request 5049 prediction. The sheer size of the World Wide Web coupled with the variation in 5050 users' navigation patterns makes this a very difficult sequence modelling 5051 problem. In this paper, the notion of probabilistic link prediction and path 5052 analysis using Markov chains is proposed and evaluated. Markov chains allow the 5053 system to dynamically model the URL access patterns that are observed in 5054 navigation logs based on the previous state. Furthermore, the Markov chain model 5055 can also be used in a generative mode to automatically obtain tours. The Markov 5056 transition matrix can be analysed further using eigenvector decomposition to 5057 obtain `personalized hubs/authorities'. The utility of the Markov chain approach 5058 is demonstrated in many domains: HTTP request prediction, system-driven adaptive 5059 Web navigation, tour generation, and detection of `personalized 5060 hubs/authorities' from user navigation profiles. The generality and power of 5061 Markov chains is a first step towards the application of powerful probabilistic 5062 models to Web path analysis and link prediction.}, 5063 author = {Ramesh R. Sarukkai}, 5064 doi = {10.1016/S1389-1286(00)00044-X}, 5065 journal = {Computer Networks}, 5066 keywords = {Adaptive navigation; HTTP request; Hubs=authorities; Link prediction; Markov chains; Tour generation}, 5067 localfile = {article/Sarukkai-2000-link-prediction.pdf}, 5068 number = {1-6}, 5069 pages = {377–386}, 5070 title = {Link prediction and path analysis using Markov chains}, 5071 volume = {33}, 5072 year = {2000} 5073 } 5074 5075 @article{Walley-2002-reconciling, 5076 abstract = {This paper describes the author's research connecting the 5077 empirical analysis of treatment response with the normative analysis of 5078 treatment choice under ambiguity. Imagine a planner who must choose a treatment 5079 rule assigning a treatment to each member of a heterogeneous population of 5080 interest. The planner observes certain covariates for each person. Each member 5081 of the population has a response function mapping treatments into a real-valued 5082 outcome of interest. Suppose that the planner wants to choose a treatment rule 5083 that maximizes the population mean outcome. An optimal rule assigns to each 5084 member of the population a treatment that maximizes mean outcome conditional on 5085 the person's observed covariates. However, identification problems in the 5086 empirical analysis of treatment response commonly prevent planners from knowing 5087 the conditional mean outcomes associated with alternative treatments; hence 5088 planners commonly face problems of treatment choice under ambiguity. The 5089 research surveyed here characterizes this ambiguity in practical settings where 5090 the planner may be able to bound but not identify the relevant conditional mean 5091 outcomes. The statistical problem of treatment choice using finite-sample data 5092 is discussed as well.}, 5093 author = {Peter Walley}, 5094 doi = {10.1016/S0378-3758(01)00204-X}, 5095 journal = {Journal of Statistical Planning and Inference}, 5096 keywords = {Conditional inference; Consistency function; Contamination neighborhood; Foundations of statistics; Frequentist principle; Imprecise Beta model; Imprecise probability; Upper probability}, 5097 localfile = {article/Walley-2002-reconciling.pdf}, 5098 pages = {35–65}, 5099 title = {Reconciling frequentist properties with the likelihood principle}, 5100 volume = {105}, 5101 year = {2002} 5102 } 5103 5104 @book{Rockafellar-1970, 5105 address = {Princeton, New Jersey}, 5106 author = {R. Tyrell Rockafellar}, 5107 publisher = {Princeton University Press}, 5108 series = {Princeton Landmarks in Mathematics}, 5109 title = {Convex Analysis}, 5110 year = {1970} 5111 } 5112 5113 @article{Cozman-2000-cn, 5114 abstract = {This paper presents a complete theory of credal networks, 5115 structures that associate convex sets of probability measures with directed 5116 acyclic graphs. Credal networks are graphical models for precise/imprecise 5117 beliefs. The main contribution of this work is a theory of credal networks that 5118 displays as much flexibility and representational power as the theory of 5119 standard Bayesian networks. Results in this paper show how to express judgements 5120 of irrelevance and independence, and how to compute inferences in credal 5121 networks. A credal network admits several extensions–several sets of 5122 probability measures comply with the constraints represented by a network. Two 5123 types of extensions are investigated. The properties of strong extensions are 5124 clarified through a new generalization of d-separation, and exact and 5125 approximate inference methods are described for strong extensions. Novel results 5126 are presented for natural extensions, and linear fractional programming methods 5127 are described for natural extensions. The paper also investigates credal 5128 networks that are defined globally through perturbations of a single network.}, 5129 author = {Fabio Gagliardi Cozman}, 5130 doi = {10.1016/S0004-3702(00)00029-1}, 5131 issn = {0004-3702}, 5132 journal = {Artificial Intelligence}, 5133 keywords = {Bayesian networks; Convex sets of probability measures; Graphical d-separation relations; Graphical models of inference; Independence relations; Lower and upper expectations; Robust Bayesian analysis}, 5134 localfile = {article/Cozman-2000-cn.pdf}, 5135 number = {2}, 5136 pages = {199–233}, 5137 title = {Credal networks}, 5138 volume = {120}, 5139 year = {2000} 5140 } 5141 5142 @book{Oliphant-2006-numpy, 5143 author = {Travis E. Oliphant}, 5144 publisher = {Trelgol Publishing}, 5145 title = {Guide to NumPy}, 5146 url = {http://www.tramy.us/numpybook.pdf}, 5147 year = {2006} 5148 } 5149 5150 @article{Daboni-1953, 5151 author = {Luciano Daboni}, 5152 journal = {Giornale dell'Istituto italiano degli attuari}, 5153 localfile = {article/Daboni-1953.pdf}, 5154 pages = {58–65}, 5155 title = {Considerazioni geometriche sulla condizione di equivalenza per una classa di eventi}, 5156 volume = {16}, 5157 year = {1953} 5158 } 5159 5160 @misc{Suppes-2003, 5161 author = {Patrick Suppes}, 5162 title = {Nonmonotonic Upper Probabilities and Quantum Entanglement}, 5163 year = {2003} 5164 } 5165 5166 @article{Ferreira-Cozman-2005-AR+, 5167 abstract = {A credal network is a graphical representation for a set of 5168 joint probability distributions. In this paper we discuss algorithms for exact 5169 and approximate inferences in credal networks. We propose a branch-and-bound 5170 framework for inference, and focus on inferences for polytree-shaped networks. 5171 We also propose a new algorithm, A/R+, for outer approximations in 5172 polytree-shaped credal networks.}, 5173 author = {José Carlos {Ferreira da Rocha} and Fabio Gagliardi Cozman}, 5174 doi = {10.1016/j.ijar.2004.10.009}, 5175 issn = {0888-613X}, 5176 journal = {International Journal of Approximate Reasoning}, 5177 localfile = {article/Ferreira-Cozman-2005-AR+.pdf}, 5178 number = {2-3}, 5179 pages = {279–296}, 5180 title = {Inference in credal networks: branch-and-bound methods and the A/R+ algorithm}, 5181 volume = {39}, 5182 year = {2005} 5183 } 5184 5185 @book{Eckel-2000-C++V2, 5186 author = {Bruce Eckel}, 5187 edition = {2}, 5188 publisher = {Prentice Hall}, 5189 title = {Thinking in C++}, 5190 volume = {2}, 5191 year = {2000} 5192 } 5193 5194 @article{Polya-1930, 5195 annote = {Bevat deel over urneproblemen}, 5196 author = {G. Pólya}, 5197 journal = {Annales de l'Institut Henri Poincaré}, 5198 localfile = {article/Polya-1930.pdf}, 5199 number = {2}, 5200 pages = {117–161}, 5201 title = {Sur quelques points de la théorie des probabilités}, 5202 url = {http://www.numdam.org/item?id=AIHP_1930__1_2_117_0}, 5203 volume = {1}, 5204 year = {1930} 5205 } 5206 5207 @inproceedings{DeBock-DeCooman-2011, 5208 abstract = {We present an efficient exact algorithm for estimating state 5209 sequences from outputs (or observations) in imprecise hidden Markov models 5210 (iHMM), where both the uncertainty linking one state to the next, and that 5211 linking a state to its output, are represented using coherent lower previsions. 5212 The notion of independence we associate with the credal network representing the 5213 iHMM is that of epistemic irrelevance. We consider as best estimates for state 5214 sequences the (Walley–Sen) maximal sequences for the posterior joint state 5215 model (conditioned on the observed output sequence), associated with a gain 5216 function that is the indicator of the state sequence. This corresponds to (and 5217 generalises) finding the state sequence with the highest posterior probability 5218 in HMMs with precise transition and output probabilities (pHMMs). We argue that 5219 the computational complexity is at worst quadratic in the length of the Markov 5220 chain, cubic in the number of states, and essentially linear in the number of 5221 maximal state sequences. For binary iHMMs, we investigate experimentally how the 5222 number of maximal state sequences depends on the model parameters.}, 5223 address = {Innsbruck, Austria}, 5224 author = {Jasper {De Bock} and Gert {De Cooman}}, 5225 booktitle = {ISIPTA'11: Proceedings of the Seventh International Symposium on Imprecise Probability: Theories and Applications}, 5226 editor = {Frank P. A. Coolen and Gert {De Cooman} and Thomas Fetz and Michael Oberguggenberger}, 5227 pages = {159–168}, 5228 publisher = {SIPTA}, 5229 title = {State sequence prediction in imprecise hidden Markov models}, 5230 year = {2011} 5231 } 5232 5233 @article{Inuiguchi-Sakawa-1997, 5234 abstract = {In this paper, we focus on a treatment of a linear 5235 programming problem with an interval objective function. From the viewpoint of 5236 the achievement rate, a new solution concept, the maximin achievement rate 5237 solution, is proposed. Nice properties of this solution are shown: a maximin 5238 achievement rate solution is necessarily optimal when a necessarily optimal 5239 solution exists, and if not, then it is still a possibly optimal solution. An 5240 algorithm for a maximin achievement rate solution is proposed based on a 5241 relaxation procedure together with a simplex method. A numerical example is 5242 given to demonstrate the proposed solution algorithm.}, 5243 author = {Masahiro Inuiguchi and M. Sakawa}, 5244 issn = {0160-5682}, 5245 journal = {Journal of the Operational Research Society}, 5246 keywords = {fractional programming}, 5247 localfile = {article/Inuiguchi-Sakawa-1997.pdf}, 5248 number = {1}, 5249 pages = {25–33}, 5250 publisher = {Palgrave Macmillan Journals on behalf of the Operational Research Society}, 5251 title = {An achievement rate approach to linear programming problems with an interval objective function}, 5252 url = {http://www.jstor.org/stable/3009940}, 5253 volume = {48}, 5254 year = {1997} 5255 } 5256 5257 @article{Williams-2007-notes, 5258 abstract = {The personalist conception of probability is often 5259 explicated in terms of betting rates acceptable to an individual. A common 5260 approach, that of de Finetti for example, assumes that the individual is willing 5261 to take either side of the bet, so that the bet is “fair” from the individual's 5262 point of view. This can sometimes be unrealistic, and leads to difficulties in 5263 the case of conditional probabilities or previsions. An alternative conception 5264 is presented in which it is only assumed that the collection of acceptable bets 5265 forms a convex cone, rather than a linear space. This leads to the more general 5266 conception of an upper conditional prevision. The main concerns of the paper are 5267 with the extension of upper conditional previsions. The main result is that any 5268 upper conditional prevision is the upper envelope of a family of additive 5269 conditional previsions.}, 5270 author = {Peter M. Williams}, 5271 doi = {10.1016/j.ijar.2006.07.019}, 5272 institution = {University of Sussex}, 5273 journal = {International Journal of Approximate Reasoning}, 5274 keywords = {Coherence; Conditional prevision; Imprecise probabilities; de Finetti}, 5275 localfile = {article/Williams-2007-notes.pdf}, 5276 pages = {366–383}, 5277 title = {Notes on conditional previsions}, 5278 volume = {44}, 5279 year = {2007} 5280 } 5281 5282 @proceedings{ISIPTA-2009, 5283 address = {Durham, United Kingdom}, 5284 editor = {Thomas Augustin and Frank P. A. Coolen and Serafin Moral and Matthias C. M. Troffaes}, 5285 organization = {SIPTA}, 5286 title = {ISIPTA '09: Proceedings of the Sixth International Symposium on Imprecise Probabilities: Theories and Applications}, 5287 year = {2009} 5288 } 5289 5290 @article{Delbaen-1974, 5291 annote = {ook op papier}, 5292 author = {Freddy Delbaen}, 5293 doi = {10.1016/0022-247X(74)90133-4}, 5294 journal = {Journal of Mathematical Analysis and Applications}, 5295 localfile = {article/Delbaen-1974.pdf}, 5296 number = {1}, 5297 pages = {210–233}, 5298 publisher = {Elsevier}, 5299 title = {Convex games and extreme points}, 5300 volume = {45}, 5301 year = {1974} 5302 } 5303 5304 @inproceedings{Quaeghebeur-2010-UAI, 5305 author = {Erik Quaeghebeur}, 5306 booktitle = {UAI-10: Proceedings of the Twenty-Sixth Conference on Uncertainty in Artificial Intelligence}, 5307 editor = {Peter Spirtes and Peter Grünwald}, 5308 isbn = {978-0-9749039-6-5}, 5309 pages = {466–473}, 5310 publisher = {AUAI Press}, 5311 title = {Characterizing the set of coherent lower previsions with a finite number of constraints or vertices}, 5312 year = {2010} 5313 } 5314 5315 @article{Jaffray-1989, 5316 author = {Jean-Yves Jaffray}, 5317 doi = {10.1016/0167-6377(89)90010-2}, 5318 journal = {Operations Research Letters}, 5319 localfile = {article/Jaffray-1989.pdf}, 5320 number = {2}, 5321 pages = {107–112}, 5322 publisher = {Elsevier}, 5323 title = {Linear utility theory for belief functions}, 5324 volume = {8}, 5325 year = {1989} 5326 } 5327 5328 @article{Williams-1980, 5329 author = {Peter M. Williams}, 5330 journal = {The British Journal for the Philosophy of Science}, 5331 localfile = {article/Williams-1980.pdf}, 5332 number = {2}, 5333 pages = {131–144}, 5334 title = {Bayesian conditionalisation and the principle of minimum information}, 5335 url = {http://www.jstor.org/stable/687182}, 5336 volume = {31}, 5337 year = {1980} 5338 } 5339 5340 @article{Huber-Strassen-1973, 5341 author = {Peter J. Huber and Volker Strassen}, 5342 doi = {10.1214/aos}, 5343 journal = {The Annals of Statistics}, 5344 localfile = {article/Huber-Strassen-1973.pdf}, 5345 pages = {251–263}, 5346 title = {Minimax tests and the Neyman-Pearson lemma for capacities}, 5347 volume = {1}, 5348 year = {1973} 5349 } 5350 5351 @article{Ioannidis-et-al-2010-afraid, 5352 author = {J. P. A. Ioannidis and Athina Tatsioni and F. B. Karassa}, 5353 doi = {10.1111/j.1365-2362.2010.02272.x}, 5354 issn = {1365-2362}, 5355 journal = {European Journal of Clinical Investigation}, 5356 localfile = {article/Ioannidis-et-al-2010-afraid.pdf}, 5357 number = {4}, 5358 pages = {285–287}, 5359 title = {Who is afraid of reviewers' comments?: Or, why anything can be published and anything can be cited}, 5360 volume = {40}, 5361 year = {2010} 5362 } 5363 5364 @techreport{kam981, 5365 author = {Milan Hladík}, 5366 institution = {KAM-DIMATIA Series}, 5367 number = {981}, 5368 title = {Interval linear programming: A survey}, 5369 year = {2010} 5370 } 5371 5372 @article{Gneiting-Raftery-2007, 5373 abstract = {Scoring rules assess the quality of probabilistic forecasts, 5374 by assigning a numerical score based on the predictive distribution and on the 5375 event or value that materializes. A scoring rule is proper if the forecaster 5376 maximizes the expected score for an observation drawn from the distributionF if 5377 he or she issues the probabilistic forecast F, rather than G ≠ F. It is strictly 5378 proper if the maximum is unique. In prediction problems, proper scoring rules 5379 encourage the forecaster to make careful assessments and to be honest. In 5380 estimation problems, strictly proper scoring rules provide attractive loss and 5381 utility functions that can be tailored to the problem at hand. This article 5382 reviews and develops the theory of proper scoring rules on general probability 5383 spaces, and proposes and discusses examples thereof. Proper scoring rules derive 5384 from convex functions and relate to information measures, entropy functions, and 5385 Bregman divergences. In the case of categorical variables, we prove a rigorous 5386 version of the Savage representation. Examples of scoring rules for 5387 probabilistic forecasts in the form of predictive densities include the 5388 logarithmic, spherical, pseudospherical, and quadratic scores. The continuous 5389 ranked probability score applies to probabilistic forecasts that take the form 5390 of predictive cumulative distribution functions. It generalizes the absolute 5391 error and forms a special case of a new and very general type of score, the 5392 energy score. Like many other scoring rules, the energy score admits a kernel 5393 representation in terms of negative definite functions, with links to 5394 inequalities of Hoeffding type, in both univariate and multivariate settings. 5395 Proper scoring rules for quantile and interval forecasts are also discussed. We 5396 relate proper scoring rules to Bayes factors and to cross-validation, and 5397 propose a novel form of cross-validation known as random-fold cross-validation. 5398 A case study on probabilistic weather forecasts in the North American Pacific 5399 Northwest illustrates the importance of propriety. We note optimum score 5400 approaches to point and quantile estimation, and propose the intuitively 5401 appealing interval score as a utility function in interval estimation that 5402 addresses width as well as coverage.}, 5403 author = {Tilmann Gneiting and Adrian E. Raftery}, 5404 doi = {10.1198/016214506000001437}, 5405 journal = {Journal of the American Statistical Association}, 5406 keywords = {Bayes factor; Bregman divergence; Brier score; Coherent; Continuous ranked probability score; Cross-validation; Entropy; Kernel score; Loss function; Minimum contrast estimation; Negative definite function; Prediction interval; Predictive distribution; Quantile forecast; Scoring rule; Skill score; Strictly proper; Utility function}, 5407 localfile = {article/Gneiting-Raftery-2007.pdf}, 5408 number = {477}, 5409 pages = {359–378}, 5410 publisher = {ASA}, 5411 title = {Strictly proper scoring rules, prediction, and estimation}, 5412 volume = {102}, 5413 year = {2007} 5414 } 5415 5416 @incollection{Seidenfeld-Schervish-Kadane-1990-decwoord, 5417 address = {Dordrecht}, 5418 author = {Teddy Seidenfeld and Mark J. Schervish and Joseph B. Kadane}, 5419 booktitle = {Acting and Reflecting: The Interdisciplinary Turn in Philosophy}, 5420 editor = {Wilfried Sieg}, 5421 pages = {143–170}, 5422 publisher = {Kluwer Academic Publishers}, 5423 series = {Synthese Library}, 5424 title = {Decisions without ordering}, 5425 volume = {211}, 5426 year = {1990} 5427 } 5428 5429 @inproceedings{Cozman-Seidenfeld-2009-graphoid, 5430 abstract = {This paper examines definitions of independence for events 5431 and variables in the context of full conditional measures; that is, when 5432 conditional probability is a primitive notion and conditioning is allowed on 5433 null events. Several independence concepts are evaluated with respect to 5434 graphoid properties; we show that properties of weak union, contraction and 5435 intersection may fail when null events are present. We propose a concept of 5436 “full” independence, characterize the form of a full conditional measure under 5437 full independence, and suggest how to build a theory of Bayesian networks that 5438 accommodates null events.}, 5439 annote = {Conference held in Amsterdam, May 2-5, 2007}, 5440 author = {Fabio Gagliardi Cozman and Teddy Seidenfeld}, 5441 booktitle = {Foundations of the Formal Sciences VI: Reasoning about Probabilities and Probabilistic Reasoning}, 5442 editor = {Benedikt Löwe and Eric Pacuit and Jan-Willem Romeijn}, 5443 publisher = {College Publications}, 5444 series = {Studies in Logic}, 5445 title = {Independence for Full Conditional Measures and their Graphoid Problems}, 5446 year = {2010} 5447 } 5448 5449 @inproceedings{Zaffalon-1999, 5450 address = {Ghent, Belgium}, 5451 author = {Marco Zaffalon}, 5452 booktitle = {ISIPTA '99: Proceedings of the First International Symposium on Imprecise probabilities and Their Applications}, 5453 editor = {Gert {De Cooman} and Fabio Gagliardi Cozman and Serafin Moral and Peter Walley}, 5454 pages = {405–414}, 5455 title = {A Credal Approach to Naive Classification}, 5456 year = {1999} 5457 } 5458 5459 @inproceedings{Quaeghebeur-2003, 5460 address = {Leuven, Belgium}, 5461 author = {Erik Quaeghebeur}, 5462 booktitle = {Proceedings of the 7th workshop on dynamics and computation: Iterated games and cooperation}, 5463 title = {Fictitious play: two viewpoints and two versions}, 5464 year = {2003} 5465 } 5466 5467 @inproceedings{Delort-BouchonMeunier-2000, 5468 author = {Jean-Yves Delort and Bernadette Bouchon-Meunier}, 5469 booktitle = {Proceedings of the Eleventh International World Wide Web Conference}, 5470 title = {Facing Uncertainty in Link Recommender Systems}, 5471 year = {2002} 5472 } 5473 5474 @article{Fukuda-2004-Minkowski-addition, 5475 abstract = {A zonotope is the Minkowski addition of line segments in Rd. 5476 The zonotope construction problem is to list all extreme points of a zonotope 5477 given by its line segments. By duality, it is equivalent to the arrangement 5478 construction problem—that is, to generate all regions of an arrangement of 5479 hyperplanes. By replacing line segments with convex V-polytopes, we obtain a 5480 natural generalization of the zonotope construction problem: the construction of 5481 the Minkowski addition of k polytopes. Gritzmann and Sturmfels studied this 5482 general problem in various aspects and presented polynomial algorithms for the 5483 problem when one of the parameters k or d is fixed. The main objective of the 5484 present work is to introduce an efficient algorithm for variable d and k. Here 5485 we call an algorithm efficient or polynomial if it runs in time bounded by a 5486 polynomial function of both the input size and the output size. The algorithm is 5487 a natural extension of a known algorithm for the zonotope construction, based on 5488 linear programming and reverse search. It is compact, highly parallelizable and 5489 very easy to implement. This work has been motivated by the use of polyhedral 5490 computation for optimal tolerance determination in mechanical engineering.}, 5491 author = {Komei Fukuda}, 5492 doi = {10.1016/j.jsc.2003.08.007}, 5493 journal = {Journal of Symbolic Computation}, 5494 keywords = {Convex polytope; Efficient algorithm; Minkowski addition; Reverse search}, 5495 localfile = {article/Fukuda-2004-Minkowski-addition.pdf}, 5496 pages = {1261–1272}, 5497 title = {From the zonotope construction to the Minkowski addition of convex polytopes}, 5498 volume = {38}, 5499 year = {2004} 5500 } 5501 5502 @misc{Doumont-2001-fundamentals, 5503 author = {Jean-luc Doumont}, 5504 title = {Fundamentals}, 5505 year = {2001} 5506 } 5507 5508 @incollection{Mura-2008-backmatter, 5509 author = {Bruno de Finetti}, 5510 doi = {10.1007/978-1-4020-8202-3}, 5511 editor = {Alberto Mura}, 5512 publisher = {Springer}, 5513 series = {Synthese Library}, 5514 title = {Back Matter}, 5515 volume = {340}, 5516 year = {2008} 5517 } 5518 5519 @article{Vicig-Zaffalon-Cozman-2007-notes, 5520 abstract = {These notes comment on Williams' fundamental essay Notes on 5521 Conditional Previsions, written as a research report in 1975 and published in 5522 the present issue. Basic aspects of that work are discussed, including 5523 historical background and relevance to the foundations of probability; examples 5524 are supplied to help understanding.}, 5525 author = {Paolo Vicig and Marco Zaffalon and Fabio Gagliardi Cozman}, 5526 doi = {10.1016/j.ijar.2006.07.018}, 5527 journal = {International Journal of Approximate Reasoning}, 5528 localfile = {article/Vicig-Zaffalon-Cozman-2007-notes.pdf}, 5529 pages = {358–365}, 5530 title = {Notes on “Notes on conditional previsions”}, 5531 volume = {44}, 5532 year = {2007} 5533 } 5534 5535 @inproceedings{DeCooman-Miranda-2004, 5536 author = {Gert {De Cooman} and Enrique Miranda}, 5537 booktitle = {Proceedings of the Tenth International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems: IPMU 2004}, 5538 pages = {451–458}, 5539 title = {A weak law of large numbers for coherent lower previsions}, 5540 year = {2004} 5541 } 5542 5543 @incollection{Neumaier-2004, 5544 author = {Arnold Neumaier}, 5545 editor = {A. Iserles}, 5546 pages = {271–369}, 5547 publisher = {Cambridge University Press}, 5548 title = {Complete Search in Continuous Global Optimization and Constraint Satisfaction}, 5549 year = {2004} 5550 } 5551 5552 @article{Nau-1992, 5553 abstract = {This paper presents a quasi-Bayesian model of subjective 5554 uncertainty in which beliefs which are represented by lower and upper 5555 probabilities qualified by numerical confidence weights. The representation is 5556 derived from a system of axioms of binary preferences which differs from 5557 standard axiom systems insofar as completeness is not assumed and transitivity 5558 is weakened. Confidence-weighted probabilities may be elicited through the 5559 acceptance of bets with limited stakes, a generalization of the operational 5560 method of de Finetti. The model is applicable to the reconciliation of 5561 inconsistent probability judgments and to the sensitivity analysis of Bayesian 5562 decision models.}, 5563 author = {Robert F. Nau}, 5564 doi = {10.1214/aos}, 5565 issn = {0090-5364}, 5566 journal = {The Annals of Statistics}, 5567 keywords = {coherence; confidence-weighted probabilities; fuzzy sets; incompletenes; lower and upper probabilities; second-order probabilities; subjective probability}, 5568 localfile = {article/Nau-1992.pdf}, 5569 month = dec, 5570 number = {4}, 5571 pages = {1737–1767}, 5572 publisher = {Institute of Mathematical Statistics}, 5573 title = {Indeterminate probabilities on finite sets}, 5574 url = {http://www.jstor.org/stable/2242366}, 5575 volume = {20}, 5576 year = {1992} 5577 } 5578 5579 @misc{Walley-1998, 5580 annote = {(used to be?) part of the Imprecise Probabilities Project geannoteerde kopie}, 5581 author = {Peter Walley}, 5582 title = {Coherent upper and lower previsions}, 5583 year = {1998} 5584 } 5585 5586 @article{Ericson-1969, 5587 abstract = {Scheffe (1958) introduced the simplex-lattice design for 5588 experiments with mixtures of q components. The purpose of this design is the 5589 empirical prediction of the response to any mixture of the components when the 5590 response depends only on the proportions of the components but not on the total 5591 amount of the mixture. In this paper an alternative to the simplex-lattice 5592 design is developed in which all the features of the design are maintained 5593 except that the pure mixtures are replaced by the (q - 1)-nary mixtures.}, 5594 annote = {with discussion}, 5595 author = {W. A. Ericson}, 5596 journal = {Journal of the Royal Statistical Society. Series B (Methodological)}, 5597 number = {2}, 5598 pages = {195–233}, 5599 title = {Subjective Bayesian Models in Sampling Finite Populations}, 5600 url = {http://links.jstor.org/sici?sici=0035-9246(1969)31:2%3C195:SBMISF%3E2.0.CO}, 5601 volume = {31}, 5602 year = {1969} 5603 } 5604 5605 @misc{Doumont-2001-graphing, 5606 author = {Jean-luc Doumont}, 5607 title = {Graphing data}, 5608 year = {2001} 5609 } 5610 5611 @article{Zimmermann-1983, 5612 abstract = {Fuzzy linear programming (FLP) was originally suggested to 5613 solve problems which could be formulated as LP-models, the parameters of which, 5614 however, were fuzzy rather than crisp numbers. It has turned out in the meantime 5615 that FLP is also well suited to solve LP-problems with several objective 5616 functions. FLP belongs to goal programming in the sense that implicitly or 5617 explicitly aspiration levels have to be defined at which the membership 5618 functions of the fuzzy sets reach their maximum or minimum. Main advantages of 5619 FLP are, that the models used are numerically very efficient and that they can 5620 in many ways be well adopted to different decision behaviors and contexts.}, 5621 author = {Hans-Jürgen Zimmermann}, 5622 doi = {10.1016/0305-0548(83)90004-7}, 5623 issn = {0305-0548}, 5624 journal = {Computers \& Operations Research}, 5625 number = {4}, 5626 pages = {291–298}, 5627 title = {Fuzzy mathematical programming}, 5628 volume = {10}, 5629 year = {1983} 5630 } 5631 5632 @misc{Knuth-Larrabee-Roberts-1987, 5633 annote = {Report based on a Stanford University course}, 5634 author = {Donald E. Knuth and Tracy Larrabee and Paul M. Roberts}, 5635 title = {Mathematical Writing}, 5636 year = {1987} 5637 } 5638 5639 @article{Bernard-2005, 5640 abstract = {The imprecise Dirichlet model (IDM) was recently proposed by 5641 Walley as a model for objective statistical inference from multinomial data with 5642 chances $\theta$. In the IDM, prior or posterior uncertainty about $\theta$ is 5643 described by a set of Dirichlet distributions, and inferences about events are 5644 summarized by lower and upper probabilities. The IDM avoids shortcomings of 5645 alternative objective models, either frequentist or Bayesian. We review the 5646 properties of the model, for both parametric and predictive inferences, and some 5647 of its recent applications to various statistical problems.}, 5648 author = {Jean-Marc Bernard}, 5649 doi = {10.1016/j.ijar.2004.10.002}, 5650 journal = {International Journal of Approximate Reasoning}, 5651 keywords = {Bayesian inference; Dirichlet distribution; Frequentist inference; IDM; Lower and upper probabilities; Predictive inference; Prior ignorance}, 5652 localfile = {article/Bernard-2005.pdf}, 5653 pages = {123–150}, 5654 title = {An introduction to the imprecise Dirichlet model for multinomial data}, 5655 volume = {39}, 5656 year = {2005} 5657 } 5658 5659 @article{Domingos-Pazzani-1997, 5660 abstract = {The simple Bayesian classifier is known to be optimal when 5661 attributes are independent given the class, but the question of whether other 5662 sufficient conditions for its optimality exist has so far not been explored. 5663 Empirical results showing that it performs surprisingly well in many domains 5664 containing clear attribute dependences suggest that the answer to this question 5665 may be positive. This article shows that, although the Bayesian classifier's 5666 probability estimates are only optimal under quadratic loss if the independence 5667 assumption holds, the classifier itself can be optimal under zero-one loss 5668 (misclassification rate) even when this assumption is violated by a wide margin. 5669 The region of quadratic-loss optimality of the Bayesian classifier is in fact a 5670 second-order infinitesimal fraction of the region of zero-one optimality. This 5671 implies that the Bayesian classifier has a much greater range of applicability 5672 than previously thought. For example, in this article it is shown to be optimal 5673 for learning conjunctions and disjunctions, even though they violate the 5674 independence assumption. Further, studies in artificial domains show that it 5675 will often outperform more powerful classifiers for common training set sizes 5676 and numbers of attributes, even if its bias is a priori much less appropriate to 5677 the domain. This article's results also imply that detecting attribute 5678 dependence is not necessarily the best way to extend the Bayesian classifier, 5679 and this is also verified empirically.}, 5680 author = {Pedro Domingos and Michael Pazzani}, 5681 doi = {10.1023/A:1007413511361}, 5682 journal = {Machine Learning}, 5683 keywords = {induction; naive bayesian classifier; optimal classification; simple bayesian classifier; with attribute dependences; zero-one loss}, 5684 localfile = {article/Domingos-Pazzani-1997.pdf}, 5685 number = {2}, 5686 pages = {103–130}, 5687 title = {On the optimality of the simple Bayesian classifier under zero-one loss}, 5688 volume = {29}, 5689 year = {1997} 5690 } 5691 5692 @article{Tessem, 5693 abstract = {Belief networks are tried as a method for propagation of 5694 singleton interval probabilities. A convex polytope representation of the 5695 interval probabilities is shown to make the problem intractable even for small 5696 parameters. A solution to this is to use the interval bounds directly in 5697 computations of the propagation algorithm. The algorithm presented leads to 5698 approximative results but has the advantage of being polynomial in time. It is 5699 shown that the method gives fairly good results.}, 5700 author = {Bjørnar Tessem}, 5701 doi = {10.1016/0888-613X(92)90006-L}, 5702 issn = {0888-613X}, 5703 journal = {International Journal of Approximate Reasoning}, 5704 number = {3-4}, 5705 pages = {95–120}, 5706 title = {Interval probability propagation}, 5707 volume = {7}, 5708 year = {1992} 5709 } 5710 5711 @article{DeCooman-1997-postheo1, 5712 abstract = {In this paper, I provide the basis for a measure- and 5713 integral-theoretic formulation of possibility theory. It is shown thai, using a 5714 general definition of possibility measures, and a generalization of Sugeno's 5715 fuzzy integral-the semi-normed fuzzy integral, or possibility integral-. a 5716 unified and consistent account can be given of many of the possibilistic results 5717 extant in the literature. The striking formal analogy between this treatment of 5718 possibility theory, using possibility integrals, and Kolmogorov's 5719 measure-theoretic formulation of probability theory, using Lebesgue integrals, 5720 is explored and exploited. I introduce and study possibilistic and fuzzy 5721 variables as possibilistic counterparts of stochastic and real stochastic 5722 variables respeclively, and develop the notion of a possibility distribution for 5723 these variables. The almost everywhere equality and dominance of fuzzy variables 5724 is defined and studied. The proof is given for a Radon-Nikodym-like theorem in 5725 possibility theory. Following the example set by the classical theory of 5726 integration, product possibility measures and multiple possibility integrals are 5727 introduced, and a Fubini-like theorem is proven. In this way, the groundwork is 5728 laid for a unifying measure- and integral-theoretic treatment of conditional 5729 possibility and possibilistic independence, discussed in more detail in Parts II 5730 and III of this series of three papers.}, 5731 author = {Gert {De Cooman}}, 5732 doi = {10.1080/03081079708945160}, 5733 journal = {International Journal of General Systems}, 5734 keywords = {Fubini-like theorem; Possibility measure; Radon-Nikodym-like theorem; fuzzy variable; possibilistic variable; possibility distribution; seminormed fuzzy integral}, 5735 localfile = {article/DeCooman-1997-postheo1.pdf}, 5736 number = {4}, 5737 pages = {291–323}, 5738 title = {Possibility theory I: the measure- and integral-theoretic groundwork}, 5739 url = {http://hdl.handle.net/1854/LU-182365}, 5740 volume = {25}, 5741 year = {1997} 5742 } 5743 5744 @book{Kallenberg-2005, 5745 author = {Olav Kallenberg}, 5746 publisher = {Springer}, 5747 series = {probability and Its Applications}, 5748 title = {Probabilistic Symmetries and Invariance Principles}, 5749 year = {2005} 5750 } 5751 5752 @article{Rommelfanger-1996, 5753 abstract = {This paper presents a survey on methods for solving fuzzy 5754 linear programs. First LP models with soft constraints are discussed. Then LP 5755 problems in which coefficients of constraints and/or of the objective function 5756 may be fuzzy are outlined. Pivotal questions are the interpretation of the 5757 inequality relation in fuzzy constraints and the meaning of fuzzy objectives. In 5758 addition to the commonly applied extended addition, based on the min-operator 5759 and used for the aggregation of the left-hand sides of fuzzy constraints and 5760 fuzzy objectives, a more flexible procedure, based on Yager's parametrized 5761 t-norm Tp, is presented. Finally practical applications of fuzzy linear programs 5762 are listed.}, 5763 author = {Heinrich Rommelfanger}, 5764 doi = {10.1016/0377-2217(95)00008-9}, 5765 issn = {0377-2217}, 5766 journal = {European Journal of Operational Research}, 5767 keywords = {Compromise solution; Extended addition of fuzzy intervals; Fuzzy sets; Inequality relation in fuzzy conslraints; Mathematical Programming}, 5768 localfile = {article/Rommelfanger-1996.pdf}, 5769 number = {3}, 5770 pages = {512–527}, 5771 title = {Fuzzy linear programming and applications}, 5772 volume = {92}, 5773 year = {1996} 5774 } 5775 5776 @misc{DeCooman-2003, 5777 annote = {Transparanten voor ISIPTA'03}, 5778 author = {Gert {De Cooman}}, 5779 title = {Theory of Imprecise Probabilities (Basic ideas)}, 5780 year = {2003} 5781 } 5782 5783 @techreport{Coolen-Augustin-2006-cNPI1, 5784 author = {Frank P. A. Coolen and Thomas Augustin}, 5785 title = {Nonparametric predictive inference for multinomial data - Notes 1 (m-functions and interval probabilities for events)}, 5786 year = {2006} 5787 } 5788 5789 @book{Walley-1991, 5790 address = {London}, 5791 author = {Peter Walley}, 5792 localfile = {book/Walley-1991-book.pdf; book/Walley-1991.pdf}, 5793 publisher = {Chapman \& Hall}, 5794 series = {Monographs on Statistics and Applied Probability}, 5795 title = {Statistical Reasoning with Imprecise Probabilities}, 5796 volume = {42}, 5797 year = {1991} 5798 } 5799 5800 @book{Prautzsch-Boehm-Paluszny-2002-Bezier, 5801 annote = {boek bij Gert}, 5802 author = {Hartmut Prautzsch and Wolfgang Boehm and Marco Paluszny}, 5803 publisher = {Springer}, 5804 series = {Mathematics and visualization}, 5805 title = {Bézier and B-spline Techniques}, 5806 year = {2002} 5807 } 5808 5809 @article{Wagner-1992-gen-probkin, 5810 author = {Carl G. Wagner}, 5811 journal = {Erkenntnis}, 5812 pages = {245–257}, 5813 title = {Generalized probability Kinematics}, 5814 volume = {36}, 5815 year = {1992} 5816 } 5817 5818 @proceedings{ICML-2002, 5819 booktitle = {Proceedings of the 19th International Conference on Machine Learning (ICML 2002)}, 5820 title = {Proceedings of the 19th International Conference on Machine Learning (ICML 2002)}, 5821 year = {2002} 5822 } 5823 5824 @phdthesis{Strobl-2008, 5825 author = {Carolin Strobl}, 5826 school = {Institut für Statistik, Fakultät für Mathematik, Informatik und Statistik, Ludwig-Maximilians-Universität München}, 5827 title = {Statistical Issues in Machine Learning – Towards Reliable Split Selection and Variable Importance Measures}, 5828 year = {2008} 5829 } 5830 5831 @article{Alexandrov-Kopteva-Kutateladze-2005-Blashke, 5832 abstract = {This is an extended version of a talk on October 4, 2004 at 5833 the research seminar “Differential geometry and applications” (headed by 5834 Academician A. T. Fomenko) at Moscow State University. The paper contains an 5835 overview of available (but far from well-known) results about the Blaschke 5836 addition of convex bodies, some new theorems on the monotonicity of the volume 5837 of convex bodies (in particular, convex polyhedra with parallel faces) as well 5838 as description of a software for visualization of polyhedra with prescribed 5839 outward normals and face areas.}, 5840 author = {Victor Alexandrov and Natalia Kopteva and S. S. Kutateladze}, 5841 journal = {Tr. Semin. Vektorn. Tenzorn. Anal.}, 5842 pages = {8–30}, 5843 title = {Blaschke addition and convex polyhedra}, 5844 volume = {26}, 5845 year = {2005} 5846 } 5847 5848 @article{Miranda-DeCooman-2007-margext, 5849 abstract = {We generalise Walley's Marginal Extension Theorem to the 5850 case of any finite number of conditional lower previsions. Unlike the procedure 5851 of natural extension, our marginal extension always provides the smallest (most 5852 conservative) coherent extensions. We show that they can also be calculated as 5853 lower envelopes of marginal extensions of conditional linear (precise) 5854 previsions. Finally, we use our version of the theorem to study the so-called 5855 forward irrelevant product and forward irrelevant natural extension of a number 5856 of marginal lower previsions.}, 5857 author = {Enrique Miranda and Gert {De Cooman}}, 5858 doi = {10.1016/j.ijar.2006.12.009}, 5859 journal = {International Journal of Approximate Reasoning}, 5860 keywords = {Coherence; Epistemic irrelevance; Forward irrelevance; Forward irrelevant natural extension; Forward irrelevant product; Imprecise probabilities; Lower previsions; Marginal extension; Natural extension}, 5861 localfile = {article/Miranda-DeCooman-2007-margext.pdf}, 5862 number = {1}, 5863 pages = {188–225}, 5864 title = {Marginal extension in the theory of coherent lower previsions}, 5865 volume = {46}, 5866 year = {2007} 5867 } 5868 5869 @misc{Lauritzen-2004a, 5870 annote = {Transparanten}, 5871 author = {Steffen L. Lauritzen}, 5872 title = {Sufficiency and Unbiased Estimation}, 5873 year = {2004} 5874 } 5875 5876 @article{Walley-1996-expert, 5877 abstract = {This paper compares four measures that have been advocated 5878 as models for uncertainty in expert systems. The measures are additive 5879 probabilities (used in the Bayesian theory), coherent lower (or upper) 5880 previsions, belief functions (used in the Dempster-Shafer theory) and 5881 possibility measures (fuzzy logic). Special emphasis is given to the theory of 5882 coherent lower previsions, in which upper and lower probabilities, expectations 5883 and conditional probabilities are constructed from initial assessments through a 5884 technique of natural extension. Mathematically, all the measures can be regarded 5885 as types of coherent lower or upper previsions, and this perspective gives some 5886 insight into the properties of belief functions and possibility measures. The 5887 measures are evaluated according to six criteria: clarity of interpretation; 5888 ability to model partial information and imprecise assessments, especially 5889 judgements expressed in natural language; rules for combining and updating 5890 uncertainty, and their justification; consistency of models and inferences; 5891 feasibility of assessment; and feasibility of computations. Each of the four 5892 measures seems to be useful in special kinds of problems, but only lower and 5893 upper previsions appear to be sufficiently general to model the most common 5894 types of uncertainty.}, 5895 annote = {geannoteerde kopie}, 5896 author = {Peter Walley}, 5897 doi = {10.1016/0004-3702(95)00009-7}, 5898 journal = {Artificial Intelligence}, 5899 keywords = {Bayesian theory; Belief functions; Conditional probability; Decision; Dempster–Shafer theory; Imprecise probabilities; Inference; Lower probability; Possibility theory; Prevision; Upper probability; lndependence}, 5900 localfile = {article/Walley-1996-expert.pdf}, 5901 pages = {1–58}, 5902 title = {Measures of uncertainty in expert systems}, 5903 volume = {83}, 5904 year = {1996} 5905 } 5906 5907 @incollection{Mura-2008-frontmatter, 5908 author = {Bruno de Finetti}, 5909 doi = {10.1007/978-1-4020-8202-3}, 5910 editor = {Alberto Mura}, 5911 publisher = {Springer}, 5912 series = {Synthese Library}, 5913 title = {Front Matter}, 5914 volume = {340}, 5915 year = {2008} 5916 } 5917 5918 @inproceedings{Quaeghebeur-DeCooman-2006-SMPS, 5919 address = {Bristol}, 5920 annote = {Proceedings of the 2006 International Workshop on Soft Methods in Probability and Statistics}, 5921 author = {Erik Quaeghebeur and Gert {De Cooman}}, 5922 booktitle = {Soft Methods for Integrated Uncertainty Modelling}, 5923 editor = {Jonathan Lawry and Enrique Miranda and A. Bugarin and S. Li and María Angeles Gil and P. Grzegorzewski and Olgierd Hryniewicz}, 5924 month = sep, 5925 organization = {Artificial Intelligence Group, University of Bristol}, 5926 pages = {211–221}, 5927 publisher = {Springer}, 5928 series = {Advances in Soft Computing}, 5929 title = {Extreme lower probabilities}, 5930 volume = {6}, 5931 year = {2006} 5932 } 5933 5934 @inproceedings{DeFinetti-1928, 5935 address = {Bologna}, 5936 author = {Bruno de Finetti}, 5937 booktitle = {Atti del congresso internationale dei matematici}, 5938 pages = {179–190}, 5939 publisher = {N. Zanichelli}, 5940 title = {Funzione caratteristica di un fenomeno aleatorio}, 5941 volume = {VI}, 5942 year = {1928} 5943 } 5944 5945 @article{Boute-2005, 5946 author = {Raymond T. Boute}, 5947 doi = {10.1145/1086642.1086647}, 5948 issn = {0164-0925}, 5949 journal = {ACM Transactions on Programming Languages and Systems}, 5950 localfile = {article/Boute-2005.pdf}, 5951 month = sep, 5952 number = {5}, 5953 pages = {988–1047}, 5954 title = {Functional declarative language design and predicate calculus}, 5955 url = {http://portal.acm.org/citation.cfm?doid=1086642.1086647}, 5956 volume = {27}, 5957 year = {2005} 5958 } 5959 5960 @inproceedings{Wallner-2005, 5961 address = {Pittsburgh, Pennsylvania}, 5962 author = {Anton Wallner}, 5963 booktitle = {ISIPTA '05: Proceedings of the Fourth International Symposium on Imprecise Probabilities and Their Applications}, 5964 editor = {Fabio Gagliardi Cozman and Robert Nau and Teddy Seidenfeld}, 5965 organization = {SIPTA}, 5966 pages = {388–395}, 5967 title = {Maximal Number of Vertices of Polytopes Defined by F-Probabilities}, 5968 year = {2005} 5969 } 5970 5971 @techreport{Augustin-2003-note, 5972 author = {Thomas Augustin}, 5973 institution = {LMU München}, 5974 title = {A Note on Lower Envelopes}, 5975 year = {2003} 5976 } 5977 5978 @article{Cozman-Walley-2005-graphoid, 5979 abstract = {This paper investigates Walley's concepts of epistemic 5980 irrelevance and epistemic independence for imprecise probability models. We 5981 study the mathematical properties of irrelevance and independence, and their 5982 relation to the graphoid axioms. Examples are given to show that epistemic 5983 irrelevance can violate the symmetry, contraction and intersection axioms, that 5984 epistemic independence can violate contraction and intersection, and that this 5985 accords with informal notions of irrelevance and independence.}, 5986 annote = {ook op papier}, 5987 author = {Fabio Gagliardi Cozman and Peter Walley}, 5988 doi = {10.1007/s10472-005-9004-z}, 5989 journal = {Annals of Mathematics and Artificial Intelligence}, 5990 localfile = {article/Cozman-Walley-2005-graphoid.pdf}, 5991 number = {1}, 5992 pages = {173–195}, 5993 title = {Graphoid properties of epistemic irrelevance and independence}, 5994 volume = {45}, 5995 year = {2005} 5996 } 5997 5998 @article{Zabell-1995, 5999 abstract = {In the 1920s the English philosopher W. E. Johnson 6000 discovered a simple characterization of the Dirichlet family of conjugate priors 6001 for a multinomial distribution having at least three categories. In the present 6002 note Johnson's result is extended to the case of a Markov exchangeable 6003 sequence.}, 6004 author = {Sandy L. Zabell}, 6005 doi = {10.1007/BF02213460}, 6006 journal = {Journal of Theoretical Probability}, 6007 keywords = {Markov exchangeable sequences; W. E. Johnson; conjugate prior; predictive probability}, 6008 localfile = {article/Zabell-1995.pdf}, 6009 number = {1}, 6010 pages = {175–178}, 6011 title = {Characterizing Markov exchangeable sequences}, 6012 volume = {8}, 6013 year = {1995} 6014 } 6015 6016 @article{Miller-1980-gamma, 6017 abstract = {This paper presents a Bayesian analysis of shape, scale, and 6018 mean of the two-parameter gamma distribution. Attention is given to conjugate 6019 and "non-informative" priors, to simplifications of the numerical analysis of 6020 posterior distributions, and to comparison of Bayesian and classical 6021 inferences.}, 6022 author = {Robert B. Miller}, 6023 issn = {0040-1706}, 6024 journal = {Technometrics}, 6025 keywords = {Bayesian analysis; Gamma distribution}, 6026 localfile = {article/Miller-1980-gamma.pdf}, 6027 number = {1}, 6028 pages = {65–69}, 6029 publisher = {American Statistical Association and American Society for Quality}, 6030 title = {Bayesian analysis of the two-parameter Gamma distribution}, 6031 url = {http://www.jstor.org/stable/1268384}, 6032 volume = {22}, 6033 year = {1980} 6034 } 6035 6036 @misc{Doumont-2001-feedback, 6037 author = {Jean-luc Doumont}, 6038 title = {Giving Feedback}, 6039 year = {2001} 6040 } 6041 6042 @book{Kotz-Balakrishnan-Johnson-2000, 6043 author = {Samuel Kotz and N. Balakrishnan and Norman L. Johnson}, 6044 edition = {second}, 6045 publisher = {Wiley}, 6046 series = {Wiley Series in Probability and Statistics}, 6047 title = {Continuous Multivariate Distributions}, 6048 volume = {1: Models}, 6049 year = {2000} 6050 } 6051 6052 @article{Fujimoto-Oshime-1994-Perron-Frobenius, 6053 abstract = {By a pointed closed convex cone K \subset of \mathbb{R}^N 6054 with interior, an order is defined in \mathbb{R}^N. Let T: K\to K be a 6055 set-valued nondecreasing subhomogeneous map. The main purpose of this paper 6056 concerns the conditions on $\lambda$>0 under which $\lambda$u ∈ T(u)+c, u ∈ K, 6057 is solvable for all c∈ K and how its solution depends on c. The homogenization 6058 of T around infinity is also introduced and is proved to leave the solvability 6059 condition for $\lambda$>0 unchanged.}, 6060 author = {Takao Fujimoto and Yorimasa Oshime}, 6061 doi = {10.1016/0304-4068(94)90028-0}, 6062 journal = {Journal of Mathematical Economics}, 6063 keywords = {Homo; Monotonicity; Nonlinear resolvent problems}, 6064 localfile = {article/Fujimoto-Oshime-1994-Perron-Frobenius.pdf}, 6065 number = {5}, 6066 pages = {475–498}, 6067 title = {The nonlinear Perron-Frobenius problem for set-valued maps in a closed convex cone in R^N}, 6068 volume = {23}, 6069 year = {1994} 6070 } 6071 6072 @misc{Doumont-2001-training, 6073 author = {Jean-luc Doumont}, 6074 title = {Training others}, 6075 year = {2001} 6076 } 6077 6078 @article{DeCooman-Aeyels-2000, 6079 abstract = {The relationship is studied between possibility and 6080 necessity measures defined on arbitrary spaces, the theory of imprecise 6081 probabilities, and elementary random set theory. It is shown how special random 6082 sets can be used to generate normal possibility and necessity measures, as well 6083 as their natural extensions. This leads to interesting alternative formulas for 6084 the calculation of these natural extensions}, 6085 author = {Gert {De Cooman} and Dirk Aeyels}, 6086 doi = {10.1109/3468.833093}, 6087 journal = {IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans}, 6088 localfile = {article/DeCooman-Aeyels-2000.pdf}, 6089 number = {2}, 6090 pages = {124–130}, 6091 publisher = {IEEE}, 6092 title = {A random set description of a possibility measure and its natural extension}, 6093 volume = {30}, 6094 year = {2000} 6095 } 6096 6097 @article{Antonucci-etal-2010-GL2U, 6098 abstract = {Credal networks generalize Bayesian networks by relaxing the 6099 requirement of precision of probabilities. Credal networks are considerably more 6100 expressive than Bayesian networks, but this makes belief updating NP-hard even 6101 on polytrees. We develop a new efficient algorithm for approximate belief 6102 updating in credal networks. The algorithm is based on an important 6103 representation result we prove for general credal networks: that any credal 6104 network can be equivalently reformulated as a credal network with binary 6105 variables; moreover, the transformation, which is considerably more complex than 6106 in the Bayesian case, can be implemented in polynomial time. The equivalent 6107 binary credal network is then updated by L2U, a loopy approximate algorithm for 6108 binary credal networks. Overall, we generalize L2U to non-binary credal 6109 networks, obtaining a scalable algorithm for the general case, which is 6110 approximate only because of its loopy nature. The accuracy of the inferences 6111 with respect to other state-of-the-art algorithms is evaluated by extensive 6112 numerical tests.}, 6113 author = {Alessandro Antonucci and Yi Sun and Cassio Polpo de Campos and Marco Zaffalon}, 6114 doi = {10.1016/j.ijar.2010.01.007}, 6115 journal = {International Journal of Approximate Reasoning}, 6116 localfile = {article/Antonucci-etal-2010-GL2U.pdf}, 6117 number = {5}, 6118 pages = {474–484}, 6119 title = {Generalized loopy 2U: a new algorithm for approximate inference in credal networks}, 6120 volume = {51}, 6121 year = {2010} 6122 } 6123 6124 @article{Krantz-Kunreuther-2007, 6125 abstract = {We propose a constructed-choice model for general decision 6126 making. The model departs from utility theory and prospect theory in its 6127 treatment of multiple goals and it suggests several different ways in which 6128 context can affect choice. It is particularly instructive to apply this model to 6129 protective decisions, which are often puzzling. Among other anomalies, people 6130 insure against non-catastrophic events, underinsure against catastrophic risks, 6131 and allow extraneous factors to influence insurance purchases and other 6132 protective decisions. Neither expected-utility theory nor prospect theory can 6133 explain these anomalies satisfactorily. To apply this model to the above 6134 anomalies, we consider many different insurance-related goals, organized in a 6135 taxonomy, and we consider the effects of context on goals, resources, plans and 6136 decision rules. The paper concludes by suggesting some prescriptions for 6137 improving individual decision making with respect to protective measures.}, 6138 annote = {ook op papier}, 6139 author = {David H. Krantz and Howard C. Kunreuther}, 6140 journal = {Judgment and Decision Making}, 6141 keywords = {catastrophic risk; decision making; goals; insurance; plans; prospect theory; protective behavior; utility theory}, 6142 localfile = {article/Krantz-Kunreuther-2007.pdf}, 6143 month = jun, 6144 number = {3}, 6145 pages = {137–168}, 6146 title = {Goals and plans in decision making}, 6147 url = {http://journal.sjdm.org/jdm7303b.pdf}, 6148 volume = {2}, 6149 year = {2007} 6150 } 6151 6152 @proceedings{AI-2004, 6153 booktitle = {AI 2004: Advances in Artificial Intelligence: 17th Australian Joint Conference on Artificial Intelligence}, 6154 editor = {Geoffrey I. Webb and Xinghuo Yu}, 6155 publisher = {Springer}, 6156 series = {Lecture Notes in AI}, 6157 title = {AI 2004: Advances in Artificial Intelligence: 17th Australian Joint Conference on Artificial Intelligence}, 6158 year = {2004} 6159 } 6160 6161 @article{Mardia-ElAtoum-1976, 6162 abstract = {The main aim of this note is to give a theoretical 6163 discussion of Bayesian inference for the von Mises-Fisher distribution. The 6164 choice of particular priors is considered and the admissibility of certain 6165 Bayesian estimators studied. For the multisample case estimators are given. Some 6166 problems of testing hypotheses are summarized in the form of posterior odds 6167 against the null hypothesis.}, 6168 author = {K. V. Mardia and S. A. M. El-Atoum}, 6169 doi = {10.1093/biomet}, 6170 journal = {Biometrika}, 6171 keywords = {Bayesian directional data analysis; Loss function}, 6172 localfile = {article/Mardia-ElAtoum-1976.pdf}, 6173 number = {1}, 6174 pages = {203–206}, 6175 publisher = {Biometrika Trust}, 6176 title = {Bayesian inference for the von Mises-Fisher distribution}, 6177 volume = {63}, 6178 year = {1976} 6179 } 6180 6181 @article{Robinson-1951, 6182 annote = {ook op papier}, 6183 author = {Julia Robinson}, 6184 journal = {The Annals of Mathematics}, 6185 localfile = {article/Robinson-1951.pdf}, 6186 number = {2}, 6187 pages = {296–301}, 6188 title = {An iterative method of solving a game}, 6189 url = {http://www.jstor.org/stable/1969530}, 6190 volume = {54}, 6191 year = {1951} 6192 } 6193 6194 @book{Kadane-Schervish-Seidenfeld-1999, 6195 abstract = {This important collection of essays is a synthesis of 6196 foundational studies in Bayesian decision theory and statistics. An overarching 6197 topic of the collection is understanding how the norms for Bayesian decision 6198 making should apply in settings with more than one rational decision maker and 6199 then tracing out some of the consequences of this turn for Bayesian statistics. 6200 There are four principal themes to the collection: cooperative, non-sequential 6201 decisions; the representation and measurement of 'partially ordered' 6202 preferences; non-cooperative, sequential decisions; and pooling rules and 6203 Bayesian dynamics for sets of probabilities. The volume will be particularly 6204 valuable to philosophers concerned with decision theory, probability, and 6205 statistics, statisticians, mathematicians, and economists.}, 6206 author = {Joseph B. Kadane and Mark J. Schervish and Teddy Seidenfeld}, 6207 publisher = {Cambridge University Press}, 6208 series = {Cambridge studies in probability, induction, and decision theory}, 6209 title = {Rethinking the foundations of statistics}, 6210 url = {http://books.google.com/books?id=SsBPTDFwnpoC}, 6211 year = {1999} 6212 } 6213 6214 @techreport{Dhillon-Sra-2003-directional, 6215 abstract = {Traditionally multi-variate normal distributions have been 6216 the staple of data modeling in most domains. For some domains, the model they 6217 provide is either inadequate or incorrect because of the disregard for the 6218 directional components of the data. We present a generative model for data that 6219 is suitable for modeling directional data (as can arise in text and gene 6220 expression clustering). We use mixtures of von Mises-Fisher distributions to 6221 model our data since the von Mises-Fisher distribution is the natural 6222 distribution for directional data. We derive an Expectation Maximization (EM) 6223 algorithm to find the maximum likelihood estimates for the parameters of our 6224 mixture model, and provide various experimental results to evaluate the 6225 “correctness” of our formulation. In this paper we also provide some of the 6226 mathematical background necessary to carry out all the derivations and to gain 6227 insight for an implementation.}, 6228 address = {Austin, Texas}, 6229 author = {Inderjit S. Dhillon and Sra Suvrit}, 6230 institution = {The University of Texas at Austin}, 6231 number = {TR-03-06}, 6232 title = {Modeling Data using Directional Distributions}, 6233 url = {http://www.cs.utexas.edu/~suvrit/work/research.html}, 6234 year = {2003} 6235 } 6236 6237 @article{Gaifman-2004, 6238 author = {Haim Gaifman}, 6239 doi = {10.1023/B:SYNT.0000029944.99888.a7}, 6240 journal = {Synthese}, 6241 localfile = {article/Gaifman-2004.pdf}, 6242 number = {1-2}, 6243 pages = {97–119}, 6244 title = {Reasoning with limited resources and assigning probabilities to arithmetical statements}, 6245 volume = {140}, 6246 year = {2004} 6247 } 6248 6249 @article{Sundberg-Wagner-1990-capacities, 6250 annote = {op papier in Wagnerbundel}, 6251 author = {Carl Sundberg and Carl G. Wagner}, 6252 journal = {Journal of Theoretical Probability}, 6253 number = {1}, 6254 pages = {159–167}, 6255 title = {Characterizations of Monotone and 2-Monotone Capacities}, 6256 volume = {5}, 6257 year = {1990} 6258 } 6259 6260 @techreport{Katzoff-1964, 6261 annote = {Second Edition ook op papier}, 6262 author = {S. Katzoff}, 6263 organization = {NASA}, 6264 title = {Clarity in technical reporting}, 6265 year = {1964} 6266 } 6267 6268 @mastersthesis{Quaeghebeur-2001, 6269 abstract = {We bestuderen een leermethode voor eindige spelen in de 6270 strategische vorm. Hierbij maken de spelers gebruik van een geschiedenis van 6271 reeds gespeelde sessies om inschattingen te maken over de waarschijnlijke 6272 strategiekeuze van een tegenspeler. Op die waarschijnlijk geachte strategiekeuze 6273 baseren de spelers zich om een eigen strategie te kiezen. We bestuderen hiervoor 6274 eerst de wetenschapsdiscipline genaamd speltheorie. We gaan hier in op 6275 kenmerkende elementen van spelen en bekijken mogelijke voorstellingswijzen. We 6276 gaan dieper in op de voorstelling van een spel in de strategische vorm. Een 6277 strategie, een geheel aan regels die de keuze van acties binnen een spel 6278 volledig bepalen, en de opbrengstfunctie, die de uitslag van een spel voor de 6279 speler vastlegt, worden gedefinieerd. We bekijken hoe we de strategieën van een 6280 spel kunnen onderverdelen en welke strategieën optimaal zijn voor een speler. Zo 6281 komen we tot volgende concepten: beste antwoord, wat de verzameling van 6282 strategieën is die de opbrengst van de speler maximaliseert voor een gegeven 6283 strategie van zijn tegenspeler; evenwicht, wat een strategiecombinatie is waar 6284 geen enkele speler er voordeel bij heeft om van strategie te veranderen; 6285 dominantie, wat een methode is om strategieën te identificeren die het best niet 6286 gespeeld worden en maximin-strategie, wat een voorzichtige strategiekeuze is. In 6287 tweede instantie bespreken we imprecieze waarschijnlijkheden, wat een 6288 onzekerheidsmodel is waar niet alleen rekening kan worden gehouden met 6289 onzekerheid, maar ook met onbepaaldheid. We gaan in op de gevolgen van 6290 rationaliteitvereisten voor dit model en zijn rekenregels. Er wordt tevens een 6291 interpretatie op basis van gokgedrag gegeven aan de grootheden die we gebruiken 6292 om waarschijnlijkheden uit te drukken. Voortbouwend op het voorgaande wordt 6293 onderzocht hoe we een beslissing kunnen maken tussen keuzes voor verschillende 6294 mogelijke strategieën. Dit leidt tot de definitie van maximale strategieën, die 6295 goede keuzes zijn voor een speler. Deze beslissingen worden gebaseerd op het 6296 Dirichletmodel, dat inschattingen weergeeft over de strategiekeuze van een 6297 tegenspeler. We leggen ook uit hoe dit model bijgesteld kan worden door 6298 verrekening van de informatie bekomen uit reeds gespeelde sessies. Door het 6299 voorgaande te combineren kunnen we de beoogde leermethode formuleren. We maken 6300 hier een onderscheid tussen een precieze methode, waarbij er geen rekening wordt 6301 gehouden met eventuele onbepaaldheid en twee imprecieze methodes, waarbij dit 6302 wel gebeurt. Uiteindelijk bekijken we de dynamica van de leermethode, namelijk 6303 de evolutie van de inschattingen van spelers en de door hen gespeelde 6304 strategieën. We onderzoeken voornamelijk onder welke voorwaarden er enkel 6305 convergentie naar een evenwicht zal optreden.}, 6306 author = {Erik Quaeghebeur}, 6307 keywords = {evenwicht; fictief spelen; imprecieze waarschijnlijkheden; leren; speltheorie}, 6308 localfile = {mastersthesis/Quaeghebeur-2001.pdf}, 6309 school = {Universiteit Gent}, 6310 title = {Speltheoretisch leren met imprecieze waarschijnlijkheden: dynamische aspecten}, 6311 url = {http://hdl.handle.net/1854/6279}, 6312 year = {2001} 6313 } 6314 6315 @inproceedings{Quaeghebeur-DeCooman-Aeyels-2005, 6316 address = {Ghent, Belgium}, 6317 author = {Erik Quaeghebeur and Gert {De Cooman} and Dirk Aeyels}, 6318 booktitle = {Proceedings of the Sixth UGent-FirW PhD Symposium}, 6319 title = {Building classifiers that cope with small training sets}, 6320 year = {2005} 6321 } 6322 6323 @book{Weichselberger-2001, 6324 address = {Heidelberg}, 6325 annote = {Unter Mitarbeit von T. Augustin und A. Wallner}, 6326 author = {Kurt Weichselberger}, 6327 publisher = {Physica-Verlag}, 6328 title = {Elementare Grundbegriffe einer allgemeineren Wahrscheinlichkeitsrechnung I: Intervallwahrscheinlichkeit als Umfassendes Konzept}, 6329 year = {2001} 6330 } 6331 6332 @proceedings{ICLMPS-1975, 6333 booktitle = {Fifth International Congress of Logic, Methodology and Philosophy of Science}, 6334 title = {Fifth International Congress of Logic, Methodology and Philosophy of Science}, 6335 year = {1975} 6336 } 6337 6338 @proceedings{UAI-1995, 6339 booktitle = {UAI-95: Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence}, 6340 editor = {Philippe Besnard and Steve Hanks}, 6341 publisher = {Morgan Kaufmann}, 6342 title = {UAI-95: Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence}, 6343 year = {1995} 6344 } 6345 6346 @article{Gaubert-Gunawardena-2004-Perron, 6347 abstract = {If A is a nonnegative matrix whose associated directed graph 6348 is strongly connected, the Perron-Frobenius theorem asserts that A has an 6349 eigenvector in the positive cone, (\mathbb{R}^+)^n. We associate a directed 6350 graph to any homogeneous, monotone function, f : (\mathbb{R}+)n \to 6351 (\mathbb{R}^+)^n, and show that if the graph is strongly connected, then f has a 6352 (nonlinear) eigenvector in (\mathbb{R}^+)^n. Several results in the literature 6353 emerge as corollaries. Our methods show that the Perron-Frobenius theorem is 6354 "really" about the boundedness of invariant subsets in the Hilbert projective 6355 metric. They lead to further existence results and open problems.}, 6356 annote = {ook op papier als arXiv preprint}, 6357 author = {Stéphane Gaubert and Jeremy Gunawardena}, 6358 journal = {Transactions of the American Mathematical Society}, 6359 keywords = {Collatz-Wielandt property; Hilbert projective met; Hilbert projective metric; nonexpansive function; nonlinear eigenvalue}, 6360 localfile = {article/Gaubert-Gunawardena-2004-Perron.pdf}, 6361 number = {12}, 6362 pages = {4931–4950}, 6363 title = {The Perron-Frobenius theorem for homogeneous, monotone functions}, 6364 url = {http://www.ams.org/journals/tran/2004-356-12/S0002-9947-04-03470-1}, 6365 volume = {356}, 6366 year = {2004} 6367 } 6368 6369 @book{Burrill-1972-measure, 6370 author = {Claude W. Burrill}, 6371 publisher = {McGraw-Hill}, 6372 title = {Measure, Integration, and Probability}, 6373 year = {1972} 6374 } 6375 6376 @article{Skulj-2009-impmarkov, 6377 abstract = {The parameters of Markov chain models are often not known 6378 precisely. Instead of ignoring this problem, a better way to cope with it is to 6379 incorporate the imprecision into the models. This has become possible with the 6380 development of models of imprecise probabilities, such as the interval 6381 probability model. In this paper we discuss some modelling approaches which 6382 range from simple probability intervals to the general interval probability 6383 models and further to the models allowing completely general convex sets of 6384 probabilities. The basic idea is that precisely known initial distributions and 6385 transition matrices are replaced by imprecise ones, which effectively means that 6386 sets of possible candidates are considered. Consequently, sets of possible 6387 results are obtained and represented using similar imprecise probability models. 6388 We first set up the model and then show how to perform calculations of the 6389 distributions corresponding to the consecutive steps of a Markov chain. We 6390 present several approaches to such calculations and compare them with respect to 6391 the accuracy of the results. Next we consider a generalisation of the concept of 6392 regularity and study the convergence of regular imprecise Markov chains. We also 6393 give some numerical examples to compare different approaches to calculations of 6394 the sets of probabilities.}, 6395 author = {Damjan Škulj}, 6396 doi = {10.1016/j.ijar.2009.06.007}, 6397 issn = {0888-613X}, 6398 journal = {International Journal of Approximate Reasoning}, 6399 keywords = {Imprecise Markov chains; Imprecise probabilities; Interval probabilities; Markov chains; Regularity}, 6400 localfile = {article/Skulj-2009-impmarkov.pdf}, 6401 number = {8}, 6402 pages = {1314–1329}, 6403 title = {Discrete time Markov chains with interval probabilities}, 6404 volume = {50}, 6405 year = {2009} 6406 } 6407 6408 @techreport{Bruening-Dennenberg-2003-belELP, 6409 annote = {Direct proof (of Choquet's implicit proof) that {0,1}-valued belief measures are the extreme points of the set of belief measures.}, 6410 author = {Martin Brüning and Dieter Denneberg}, 6411 institution = {Universität Bremen}, 6412 title = {The $\sigma$-additive Möbius Transform of Belief Measures via Choquet's Theorem}, 6413 year = {2003} 6414 } 6415 6416 @inproceedings{DeCooman-Miranda-Quaeghebeur-2007-ISIPTA, 6417 abstract = {We consider immediate predictive inference, where a subject, 6418 using a number of observations of a finite number of exchangeable random 6419 variables, is asked to coherently model his beliefs about the next observation, 6420 in terms of a predictive lower prevision. We study when such predictive lower 6421 previsions are representation insensitive, meaning that they are essentially 6422 independent of the choice of the (finite) set of possible values for the random 6423 variables. Such representation insensitive predictive models have very 6424 interesting properties, and among such models, the ones produced by the 6425 Imprecise Dirichlet-Multinomial Model are quite special in a number of ways.}, 6426 address = {Prague, Czech Republic}, 6427 author = {Gert {De Cooman} and Enrique Miranda and Erik Quaeghebeur}, 6428 editor = {Gert {De Cooman} and Jiřina Vejnarová and Marco Zaffalon}, 6429 keywords = {coherence; exchangeability; immediate prediction}, 6430 organization = {SIPTA}, 6431 title = {Immediate prediction under exchangeability and represenation insensitivity}, 6432 year = {2007} 6433 } 6434 6435 @article{Aitchison-1964-tolerance, 6436 abstract = {In the theory of statistical tolerance regions, as usually 6437 presented in frequentist terms, there are inherent difficulties of formulation, 6438 development and interpretation. The present paper re-examines the basic problem 6439 from a Bayesian point of view and suggests that such an approach provides a set 6440 of widely applicable, mathematically tractable tools, often more tailored to the 6441 requirements of users than the corresponding frequentist tools. For the 6442 one-dimensional case, Bayesian intervals are quoted for a number of standard 6443 distributions and prior densities, and the customary feature of a Bayesian 6444 analysis–that special prior densities give rise to standard frequentist 6445 results–is briefly demonstrated. A problem which seems to be of greater 6446 practical significance, namely the selection of an optimum tolerance region from 6447 a set of possible tolerance regions, is also investigated and the overwhelming 6448 advantages of the Bayesian approach are indicated.}, 6449 author = {J. Aitchison}, 6450 journal = {Journal of the Royal Statistical Society. Series B (Methodological)}, 6451 localfile = {article/Aitchison-1964-tolerance.pdf}, 6452 number = {2}, 6453 pages = {161–175}, 6454 title = {Two Papers on the Comparison of Bayesian and Frequentist Approaches to Statistical Problems of Prediction: Bayesian Tolerance Regions}, 6455 url = {http://links.jstor.org/stable/2984416}, 6456 volume = {26}, 6457 year = {1964} 6458 } 6459 6460 @article{Baroni-Vicig-2005-interchange, 6461 abstract = {This paper addresses the problem of exchanging uncertainty 6462 assessments in multi-agent systems. Since it is assumed that each agent might 6463 completely ignore the internal representation of its partners, a common 6464 interchange format is needed. We analyze the case of an interchange format 6465 deﬁned by means of imprecise probabilities, pointing out the reasons of this 6466 choice. A core problem with the interchange format concerns transformations from 6467 imprecise probabilities into other formalisms (in particular, precise 6468 probabilities, possibilities, belief functions). We discuss this so far little 6469 investigated question, analyzing how previous proposals, mostly regarding 6470 special instances of imprecise probabilities, would ﬁt into this problem. We 6471 then propose some general transformation procedures, which take also account of 6472 the fact that information can be partial, i.e. may concern an arbitrary (ﬁnite) 6473 set of events.}, 6474 author = {Pietro Baroni and Paolo Vicig}, 6475 doi = {10.1016/j.ijar.2005.03.001}, 6476 journal = {International Journal of Approximate Reasoning}, 6477 keywords = {Imprecise probability theory; Multi-agent systems; Partial possibilities; Pignistic probability; Uncertainty transformations}, 6478 localfile = {article/Baroni-Vicig-2005-interchange.pdf}, 6479 pages = {147–180}, 6480 title = {An uncertainty interchange format with imprecise probabilities}, 6481 volume = {40}, 6482 year = {2005} 6483 } 6484 6485 @book{Holmes-1975, 6486 address = {New York}, 6487 author = {Richard B. Holmes}, 6488 number = {24}, 6489 publisher = {Springer-Verlag}, 6490 series = {Graduate Texts in Mathematics}, 6491 title = {Geometric Functional Analysis and its Applications}, 6492 year = {1975} 6493 } 6494 6495 @incollection{Mura-2008-ch12, 6496 author = {Bruno de Finetti}, 6497 doi = {10.1007/978-1-4020-8202-3}, 6498 editor = {Alberto Mura}, 6499 publisher = {Springer}, 6500 series = {Synthese Library}, 6501 title = {Complete additivity and zero probabilities}, 6502 volume = {340}, 6503 year = {2008} 6504 } 6505 6506 @misc{Walley-0a, 6507 annote = {written notes}, 6508 author = {Peter Walley}, 6509 title = {The theory of natural extension} 6510 } 6511 6512 @article{Cooman2007, 6513 author = {Gert {De Cooman}}, 6514 number = {1556}, 6515 title = {Representing and assessing exchangeable lower previsions}, 6516 year = {2007} 6517 } 6518 6519 @article{Wasserman-Kadane-1992, 6520 abstract = {One method for evaluating the sensitivity of a Bayesian 6521 analysis is to embed the prior into a class of priors. Then bounds on prior and 6522 posterior quantities of interest must be computed. This approach to inference, 6523 often called robust Bayesian inference, has received much attention lately. 6524 Implementing robust Bayesian methods entails difficult computations, especially 6525 if the parameter space is high dimensional. In this article we develop a Monte 6526 Carlo approach to computing these bounds and also explore some interesting 6527 theoretical properties of certain classes of priors. The methods can be useful 6528 in other situations in which bounds on expectations are required.}, 6529 author = {Larry Wasserman and Joseph B. Kadane}, 6530 issn = {0162-1459}, 6531 journal = {Journal of the American Statistical Association}, 6532 localfile = {article/Wasserman-Kadane-1992.pdf}, 6533 number = {418}, 6534 pages = {516–522}, 6535 publisher = {American Statistical Association}, 6536 title = {Computing bounds on expectations}, 6537 url = {http://www.jstor.org/stable/2290285}, 6538 volume = {87}, 6539 year = {1992} 6540 } 6541 6542 @article{Walley-2000-towards, 6543 author = {Peter Walley}, 6544 doi = {10.1016/S0888-613X(00)00031-1}, 6545 journal = {International Journal of Approximate Reasoning}, 6546 keywords = {Choquet capacity; Comparative probability; coherence; credal sets; desirable gambles; foundations of probability; interval-valued probability; lower prevision; lower probability; partial preference ordering; uncertainty measures}, 6547 localfile = {article/Walley-2000-towards.pdf}, 6548 number = {2-3}, 6549 pages = {125–148}, 6550 title = {Towards a unified theory of imprecise probability}, 6551 volume = {24}, 6552 year = {2000} 6553 } 6554 6555 @article{Diaconis-Zabell-1982, 6556 author = {Persi Diaconis and Sandy L. Zabell}, 6557 issn = {0162-1459}, 6558 journal = {Journal of the American Statistical Association}, 6559 localfile = {article/Diaconis-Zabell-1982.pdf}, 6560 number = {380}, 6561 pages = {822–830}, 6562 publisher = {American Statistical Association}, 6563 title = {Updating subjective probability}, 6564 url = {http://www.jstor.org/stable/2287313}, 6565 volume = {77}, 6566 year = {1982} 6567 } 6568 6569 @inproceedings{Lemmer-Kyburg-1991, 6570 author = {John F. Lemmer and Jr. Henry E. Kyburg}, 6571 booktitle = {AAAI-91 Proceedings}, 6572 pages = {488–493}, 6573 title = {Conditions for the existence of belief functions corresponding to intervals of beliefs}, 6574 year = {1991} 6575 } 6576 6577 @article{Johnson-1932, 6578 author = {W. E. Johnson}, 6579 issn = {0026-4423}, 6580 journal = {Mind}, 6581 localfile = {article/Johnson-1932.pdf}, 6582 number = {164}, 6583 pages = {409–423}, 6584 publisher = {Oxford University Press on behalf of the Mind Association}, 6585 title = {Probability: The Deductive and Inductive Problems}, 6586 url = {http://www.jstor.org/stable/2250183}, 6587 volume = {41}, 6588 year = {1932} 6589 } 6590 6591 @inproceedings{Moral-Wilson-1996, 6592 annote = {ook op papier}, 6593 author = {Serafín Moral and Nic Wilson}, 6594 booktitle = {Proceedings of the Sixth International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems: IPMU 96}, 6595 pages = {1337–1344}, 6596 title = {Importance sampling algorithms for the calculation of Dempster-Shafer belief}, 6597 volume = {3}, 6598 year = {1996} 6599 } 6600 6601 @proceedings{ISIPTA-2007, 6602 address = {Prague, Czech Republic}, 6603 editor = {Gert {De Cooman} and Jiřina Vejnarová and Marco Zaffalon}, 6604 localfile = {proceedings/ISIPTA-2007.pdf}, 6605 organization = {SIPTA}, 6606 publisher = {Action M Agency for SIPTA}, 6607 title = {ISIPTA '07: Proceedings of the Fifth International Symposium on Imprecise Probabilities: Theories and Applications}, 6608 url = {http://www.sipta.org/isipta07/proceedings/proceedings-optimised.pdf}, 6609 year = {2007} 6610 } 6611 6612 @article{Cano-etal-2007-cn, 6613 abstract = {This paper proposes two new algorithms for inference in 6614 credal networks. These algorithms enable probability intervals to be obtained 6615 for the states of a given query variable. The first algorithm is approximate and 6616 uses the hill-climbing technique in the Shenoy-Shafer architecture to propagate 6617 in join trees ; the second is exact and is a modification of Rocha and Cozman's 6618 branch-and-bound algorithm, but applied to general directed acyclic graphs.}, 6619 author = {Andrés Cano and Manuel Gómez and Serafín Moral and Joaquín Abellán}, 6620 doi = {10.1016/j.ijar.2006.07.020}, 6621 issn = {0888-613X}, 6622 journal = {International Journal of Approximate Reasoning}, 6623 keywords = {Bayesian networks; branch-and-bound algorithms; credal network; hill-climbing; probability intervals; strong independence}, 6624 localfile = {article/Cano-etal-2007-cn.pdf}, 6625 number = {3}, 6626 pages = {261–280}, 6627 title = {Hill-climbing and branch-and-bound algorithms for exact and approximate inference in credal networks}, 6628 volume = {44}, 6629 year = {2007} 6630 } 6631 6632 @article{Lo-1986-finite-sampling, 6633 author = {Albert Y. Lo}, 6634 doi = {10.1214/aos}, 6635 journal = {The Annals of Statistics}, 6636 localfile = {article/Lo-1986-finite-sampling.pdf}, 6637 number = {3}, 6638 pages = {1226–1233}, 6639 publisher = {Institute of Mathematical Statistics}, 6640 title = {Bayesian statistical inference for sampling a finite population}, 6641 volume = {14}, 6642 year = {1986} 6643 } 6644 6645 @article{Hall-Lawry-2004-approx, 6646 abstract = {Random set theory provides a convenient mechanism for 6647 representing uncertain knowledge including probabilistic and set-based 6648 information, and extending it through a function. This paper focuses upon the 6649 situation when the available information is in terms of coherent lower and upper 6650 probabilities, which are encountered, for example, when a probability 6651 distribution is speciﬁed by interval parameters. We propose an Iterative 6652 Rescaling Method (IRM) for constructing a random set with corresponding belief 6653 and plausibility measures that are a close outer approximation to the lower and 6654 upper probabilities. The approach is compared with the discrete approximation 6655 method of Williamson and Downs (sometimes referred to as the p-box), which 6656 generates a closer approximation to lower and upper cumulative probability 6657 distributions but in most cases a less accurate approximation to the lower and 6658 upper probabilities on the remainder of the power set. Four combination methods 6659 are compared by application to example random sets generated using the IRM.}, 6660 author = {Jim W. Hall and Jonathan Lawry}, 6661 doi = {10.1016/j.ress.2004.03.005}, 6662 journal = {Reliability Engineering \& System Safety}, 6663 keywords = {Coherent lower and upper probabilities; Dempster–Shafer theory; Iterative rescaling method; Möbius inversion; Random set theory; p-Box}, 6664 localfile = {article/Hall-Lawry-2004-approx.pdf}, 6665 pages = {89–101}, 6666 title = {Generation, combination and extension of random set approximations to coherent lower and upper probabilities}, 6667 volume = {85}, 6668 year = {2004} 6669 } 6670 6671 @article{Xie-Beerel-1998-stateclassif, 6672 abstract = {This paper presents an efficient method for state 6673 classification of finite-state Markov chains using binary-decision diagram-based 6674 symbolic techniques. The method exploits the fundamental properties of a Markov 6675 chain and classifies the state space by iteratively applying reachability 6676 analysis. We compare our method with the state-of-the-art technique, which 6677 requires the transitive closure of the transition relation of a Markov chain. 6678 Experiments in over a dozen synchronous and asynchronous systems and queueing 6679 networks demonstrate that our method dramatically reduces the CPU time needed 6680 and solves much larger problems because of the reduced memory requirements}, 6681 annote = {Geannoteerde versie op papier}, 6682 author = {Aiguo Xie and P. A. Beerel}, 6683 doi = {10.1109/43.736573}, 6684 issn = {0278-0070}, 6685 journal = {IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems}, 6686 keywords = {BDD-based symbolic techniques; CPU time reduction; Markov processes; asynchronous systems; binary decision diagrams; binary-decision diagram; circuit analysis computing; finite-state Markov chains; queueing networks; reachability analysis; state classification; state space; synchronous systems}, 6687 localfile = {article/Xie-Beerel-1998-stateclassif.pdf}, 6688 number = {12}, 6689 pages = {1334–1339}, 6690 title = {Efficient state classification of finite-state Markov chains}, 6691 volume = {17}, 6692 year = {1998} 6693 } 6694 6695 @article{Haldane-1948, 6696 author = {J. B. S. Haldane}, 6697 journal = {Biometrika}, 6698 localfile = {article/Haldane-1948.pdf}, 6699 number = {3–4}, 6700 pages = {297–300}, 6701 title = {The precision of observed values of small frequencies}, 6702 url = {http://www.jstor.org/stable/2332350}, 6703 volume = {35}, 6704 year = {1948} 6705 } 6706 6707 @article{Pinkus-2005-approx, 6708 abstract = {Approximation theory is concerned with the ability to 6709 approximate functions by simpler and more easily calculated functions. The first 6710 question we ask in approximation theory concerns the possibility of 6711 approximation. Is the given family of functions from which we plan to 6712 approximate dense in the set of functions we wish to approximate? In this work, 6713 we survey some of the main density results and density methods.}, 6714 archiveprefix = {arXiv}, 6715 arxivid = {math/0501328}, 6716 author = {Allan Pinkus}, 6717 eprint = {0501328}, 6718 journal = {Surveys in Approximation Theory}, 6719 localfile = {article/Pinkus-2005-approx.pdf}, 6720 pages = {1–45}, 6721 primaryclass = {math}, 6722 title = {Density in Approximation Theory}, 6723 url = {http://www.math.technion.ac.il/sat/papers/1}, 6724 volume = {1}, 6725 year = {2005} 6726 } 6727 6728 @book{Hatcher-2002, 6729 author = {Allan Hatcher}, 6730 publisher = {Cambridge University Press}, 6731 title = {Algebraic Topology}, 6732 year = {2002} 6733 } 6734 6735 @inproceedings{DeCooman-Quaeghebeur-Miranda-2007-ISI, 6736 abstract = {This paper deals with belief models, and in particular lower 6737 previsions, for both (finite) collections and (infinite) sequences of 6738 exchangeable random variables taking a finite number of values. When such 6739 collections or sequences are assumed to be exchangeable, this more or less means 6740 that their specific order is irrelevant. We show that exchangeable lower 6741 previsions can be written as a combination of (i) a coherent prevision 6742 expressing that permutations of realisations of such collections or sequences 6743 are considered equally likely, and (ii) a coherent lower prevision for the 6744 `frequency' of occurrence of the different values the random variables can take. 6745 This is the essence of representation in de Finetti's sense: we generalise his 6746 results to coherent lower previsions, both for finite collections and infinite 6747 sequences. We also solve a more practical problem: how to extend a number of 6748 lower prevision assessments to an exchangeable lower prevision that is as 6749 conservative as possible.}, 6750 address = {Lisboa, Portugal}, 6751 author = {Gert {De Cooman} and Erik Quaeghebeur and Enrique Miranda}, 6752 booktitle = {Bulletin of the International Statistical Institute 56th Session – Proceedings}, 6753 number = {1556}, 6754 organization = {International Statistical Institute}, 6755 title = {Representing and assessing exchangeable lower previsions}, 6756 year = {2007} 6757 } 6758 6759 @inproceedings{Skulj-2007-Markov, 6760 abstract = {In Markov chain theory a stochastic matrix P is regular if 6761 some matrix power P^n contains only strictly positive elements. Regularity of 6762 transition matrix of a Markov chain guarantees the existence of a unique 6763 invariant distribution which is also the limiting distribution. In the present 6764 paper a similar result is shown for the generalized Markov chain model that 6765 replaces classical probabilities with interval probabilities. We generalize the 6766 concept of regularity and show that for a regular interval transition matrix 6767 sets of probabilities corresponding to consecutive steps of a Markov chain 6768 converge to a unique limiting set of distributions that only depends on 6769 transition matrix and is independent of the initial distribution. A similar 6770 convergence result is also shown for approximations of the invariant set.}, 6771 author = {Damjan Škulj}, 6772 keywords = {Markov chain; interval probability}, 6773 pages = {405–414}, 6774 title = {Regular finite Markov chains with interval probabilities}, 6775 year = {2007} 6776 } 6777 6778 @article{Dempster-1967, 6779 abstract = {A multivalued mapping from a space X to a space S carries a 6780 probability measure defined over subsets of X into a system of upper and lower 6781 probabilities over subsets of S. Some basic properties of such systems are 6782 explored in Sections 1 and 2. Other approaches to upper and lower probabilities 6783 are possible and some of these are related to the present approach in Section 3. 6784 A distinctive feature of the present approach is a rule for conditioning, or 6785 more generally, a rule for combining sources of information, as discussed in 6786 Sections 4 and 5. Finally, the context in statistical inference from which the 6787 present theory arose is sketched briefly in Section 6.}, 6788 annote = {ook op papier}, 6789 author = {Arthur P. Dempster}, 6790 journal = {The Annals of Mathematical Statistics}, 6791 localfile = {article/Dempster-1967.pdf}, 6792 number = {2}, 6793 pages = {325–339}, 6794 publisher = {Springer}, 6795 title = {Upper and lower probabilities induced by a multivalued mapping}, 6796 url = {http://www.jstor.org/stable/2239146}, 6797 volume = {38}, 6798 year = {1967} 6799 } 6800 6801 @inproceedings{Quaeghebeur-DeCooman-2005, 6802 address = {Pittsburgh, Pennsylvania}, 6803 author = {Erik Quaeghebeur and Gert {De Cooman}}, 6804 booktitle = {ISIPTA '05: Proceedings of the Fourth International Symposium on Imprecise Probabilities and Their Applications}, 6805 editor = {Fabio Gagliardi Cozman and Robert Nau and Teddy Seidenfeld}, 6806 organization = {SIPTA}, 6807 pages = {287–296}, 6808 title = {Imprecise probability models for inference in exponential families}, 6809 year = {2005} 6810 } 6811 6812 @inproceedings{Verheest-Hellberg-Mace-1998, 6813 annote = {reprint}, 6814 author = {Frank Verheest and Manfred A. Hellberg and Richard L. Mace}, 6815 booktitle = {AIP Conference Proceedings}, 6816 organization = {American Institute of Physics}, 6817 title = {New aspects of the Jeans instability in dusty plasmas}, 6818 year = {1998} 6819 } 6820 6821 @inproceedings{Alessio-Zaffalon-Miranda-2009-filtering, 6822 abstract = {We extend hidden Markov models for continuous variables 6823 taking into account imprecision in our knowledge about the probabilistic 6824 relationships involved. To achieve that, we consider sets of probabilities, also 6825 called coherent lower previsions. In addition to the general formulation, we 6826 study in detail a particular case of interest: linear-vacuous mixtures. We also 6827 show, in a practical case, that our extension outperforms the Kalman filter when 6828 modelling errors are present in the system.}, 6829 address = {Seattle, Washington}, 6830 annote = {ook op papier}, 6831 author = {Alessio Benavoli and Marco Zaffalon and Enrique Miranda}, 6832 booktitle = {FUSION 2009: Proceedings of the 12th International Conference on Information Fusion.}, 6833 organization = {IEEE}, 6834 pages = {1743–1750}, 6835 title = {Reliable hidden Markov model filtering through coherent lower previsions}, 6836 year = {2009} 6837 } 6838 6839 @article{Wagner-2004-modus-tollens, 6840 annote = {op papier in Wagnerbundel}, 6841 author = {Carl G. Wagner}, 6842 journal = {British Journal of the Philosophy of Science}, 6843 pages = {747–753}, 6844 title = {Modus Tollens probabilized}, 6845 volume = {55}, 6846 year = {2004} 6847 } 6848 6849 @article{VantVeer-etal-2002, 6850 annote = {ook op papier}, 6851 author = {Laura J. {van 't Veer} and Hongyue Dai and Marc J. {Van de Vijver} and Yudong D. He and Augustinus A. M. Hart and Mao Mao and Hans L. Peterse and Karin {Van der Kooy} and Matthew J. Marton and Anke T. Witteveen and George J. Schreiber and Ron M. Kerkhoven and Chris Roberts and Peter S. Linsley and René Bernards and Stephen H. Friend}, 6852 doi = {10.1038/415530a}, 6853 journal = {Nature}, 6854 localfile = {article/VantVeer-etal-2002.pdf}, 6855 number = {6871}, 6856 pages = {530–536}, 6857 publisher = {Nature Publishing Group}, 6858 title = {Gene expression profiling predicts clinical outcome of breastcancer}, 6859 volume = {415}, 6860 year = {2002} 6861 } 6862 6863 @article{Jamison-Lodwick-2001, 6864 abstract = {In this paper we begin with a standard form of the linear 6865 programming problem. We replace each constant in the problem with a fuzzy 6866 number. We then reformat the objective and constraints into an unconstrained 6867 fuzzy function by penalizing the objective for possible constraint violations. 6868 The range of this fuzzy function lies in the space of fuzzy numbers. The 6869 objective is then redefined as optimizing the expected midpoint of the image of 6870 this fuzzy function. We show that this objective defines a concave function 6871 which, therefore, can be maximized globally. We present an algorithm for finding 6872 the optimum.}, 6873 author = {K. David Jamison and Weldon A. Lodwick}, 6874 doi = {10.1016/S0165-0114(99)00082-2}, 6875 issn = {0165-0114}, 6876 journal = {Fuzzy Sets and Systems}, 6877 keywords = {Fuzzy function; Fuzzy number; Linear programming; possibility distribution}, 6878 localfile = {article/Jamison-Lodwick-2001.pdf}, 6879 number = {1}, 6880 pages = {97–110}, 6881 title = {Fuzzy linear programming using a penalty method}, 6882 volume = {119}, 6883 year = {2001} 6884 } 6885 6886 @misc{Doumont-2001-persuading, 6887 author = {Jean-luc Doumont}, 6888 title = {Persuading others}, 6889 year = {2001} 6890 } 6891 6892 @article{Steuer-1981, 6893 abstract = {This paper presents three algorithms for solving linear 6894 programming problems in which some or all of the objective function coefficients 6895 are specified in terms of intervals. Which algorithm is applicable depends upon 6896 (a) the number of interval objective function coefficients, (b) the number of 6897 nonzero objective function coefficients, and (c) whether or not the feasible 6898 region is bounded. The algorithms output all extreme points and unbounded edge 6899 directions that are "multiparametrically optimal" with respect to the ranges 6900 placed on the objective function coefficients. The algorithms are most suitable 6901 to linear programs in which the objective function coefficients are 6902 deterministic but are likely to vary from time period to time period (as for 6903 example in blending problems).}, 6904 author = {Ralph E. Steuer}, 6905 issn = {0364-765X}, 6906 journal = {Mathematics of Operations Research}, 6907 localfile = {article/Steuer-1981.pdf}, 6908 number = {3}, 6909 pages = {333–348}, 6910 publisher = {INFORMS}, 6911 title = {Algorithms for linear programming problems with interval objective function coefficients}, 6912 url = {http://www.jstor.org/stable/3689177}, 6913 volume = {6}, 6914 year = {1981} 6915 } 6916 6917 @proceedings{Klee-1963, 6918 editor = {V. L. {Klee, Jr. }}, 6919 publisher = {American Mathematical Society}, 6920 series = {Proceedings of Symposia in Pure Mathematics}, 6921 title = {Convexity: Proceedings of the Seventh Symposium in Pure Mathematics of the American Mathematical Society}, 6922 url = {http://books.google.com/books?id=MuEFJR7Ek4EC}, 6923 year = {1963} 6924 } 6925 6926 @book{Grinstead-Snell-2006-probintro, 6927 annote = {GNU FDL version, source available}, 6928 author = {Charles M. Grinstead and J. Laurie Snell}, 6929 publisher = {American Mathematical Society}, 6930 title = {Introduction to Probability}, 6931 year = {2006} 6932 } 6933 6934 @article{Haddad-Moreaux-2007, 6935 abstract = {Performance evaluation of complex systems is a critical 6936 issue and bounds computation provides confidence about service quality, 6937 reliability, etc. of such systems. The stochastic ordering theory has generated 6938 a lot of works on bounds computation. Maximal lower and minimal upper bounds of 6939 a Markov chain by a st-monotone one exist and can be efficiently computed. In 6940 the present work, we extend simultaneously this last result in two directions. 6941 On the one hand, we handle the case of a maximal monotone lower bound of a 6942 family of Markov chains where the coefficients are given by numerical intervals. 6943 On the other hand, these chains are sub-chains associated to sub-stochastic 6944 matrices. We prove the existence of this maximal bound and we provide polynomial 6945 time algorithms to compute it both for discrete and continuous Markov chains. 6946 Moreover, it appears that the bounding sub-chain of a family of strictly 6947 sub-stochastic ones is not necessarily strictly sub-stochastic. We establish a 6948 characterization of the families of sub-chains for which these bounds are 6949 strictly sub-stochastic. Finally, we show how to apply these results to a 6950 classical model of repairable system. A forthcoming paper will present detailed 6951 numerical results and comparison with other methods.}, 6952 author = {Serge Haddad and Patrice Moreaux}, 6953 doi = {10.1016/j.ejor.2005.08.016}, 6954 issn = {0377-2217}, 6955 journal = {European Journal of Operational Research}, 6956 keywords = {Markov process; Stochastic bound; Stochastic process; Strong stochastic ordering; Sub-Markov chain}, 6957 localfile = {article/Haddad-Moreaux-2007.pdf}, 6958 number = {2}, 6959 pages = {999–1015}, 6960 title = {Sub-stochastic matrix analysis for bounds computation–Theoretical results}, 6961 volume = {176}, 6962 year = {2007} 6963 } 6964 6965 @article{Boratynska-1997, 6966 abstract = {The problem of estimating the unknown parameter of a 6967 one-parameter exponential family with the conjugate prior is considered. Some 6968 uncertainty about the prior is assumed by introducing a class of priors Gamma. 6969 The most robust and conditional Gamma-minimax estimators are constructed. The 6970 situations when those estimators coincide are presented. The paper is a 6971 generalization of the result for the Poisson distribution obtained in Mezarski 6972 and Zielinski (1991).}, 6973 annote = {ook op papier}, 6974 author = {Agata Boratyńska}, 6975 doi = {10.1016/S0167-7152(97)00060-6}, 6976 journal = {Statistics \& Probability Letters}, 6977 keywords = {Bayes estimators; classes of priors; one-parameter exponential family; robust Bayesian estimation}, 6978 localfile = {article/Boratynska-1997.pdf}, 6979 number = {2}, 6980 pages = {173–178}, 6981 publisher = {Elsevier}, 6982 title = {Stability of Bayesian inference in exponential families}, 6983 volume = {36}, 6984 year = {1997} 6985 } 6986 6987 @article{Schervish-Seidenfeld-Kadane-2002-incoherence, 6988 author = {Mark J. Schervish and Teddy Seidenfeld and Joseph B. Kadane}, 6989 journal = {Sankhya Series A}, 6990 localfile = {article/Schervish-Seidenfeld-Kadane-2002-incoherence.pdf}, 6991 number = {3}, 6992 pages = {561–587}, 6993 title = {Measuring Incoherence}, 6994 url = {http://repository.cmu.edu/statistics/29}, 6995 volume = {64}, 6996 year = {2002} 6997 } 6998 6999 @article{Roy-1987, 7000 author = {Nina M. Roy}, 7001 doi = {10.2307/2322725}, 7002 journal = {The American Mathematical Monthly}, 7003 localfile = {article/Roy-1987.pdf}, 7004 number = {5}, 7005 pages = {409–422}, 7006 title = {Extreme points of convex sets in infinite dimensional spaces}, 7007 url = {http://www.jstor.org/stable/2322725}, 7008 volume = {94}, 7009 year = {1987} 7010 } 7011 7012 @inproceedings{Walter-Augustin-Peters-2007-regression, 7013 abstract = {Regression is the central concept in applied statistics for 7014 analyzing multivariate, heterogenous data: The influence of a group of variables 7015 on one other variable is quantified by the regression parameter $\beta$. In this 7016 paper, we extend standard Bayesian inference on $\beta$ in linear regression 7017 models by considering imprecise conjugated priors. Inspired by a variation and 7018 an extension of a method for inference in i.i.d. exponential families presented 7019 at ISIPTA'05 by Quaeghebeur and de Cooman, we develop a general framework for 7020 handling linear regression models including analysis of variance models, and 7021 discuss obstacles in direct implementation of the method. Then properties of the 7022 interval-valued point estimates for a two-regressor model are derived and 7023 illustrated with simulated data. As a practical example we take a small data set 7024 from the AIRGENE study and consider the influence of age and body mass index on 7025 the concentration of an inflammation marker.}, 7026 address = {Prague, Czech Republic}, 7027 author = {Gero Walter and Thomas Augustin and Annette Peters}, 7028 editor = {Gert {De Cooman} and Jiřina Vejnarová and Marco Zaffalon}, 7029 organization = {SIPTA}, 7030 title = {Linear Regression Analysis under Sets of Conjugate Priors}, 7031 year = {2007} 7032 } 7033 7034 @article{Seidenfeld-Wasserman-1993, 7035 abstract = {Suppose that a probability measure P is known to lie in a 7036 set of probability measures M. Upper and lower bounds on the probability of any 7037 event may then be computed. Sometimes, the bounds on the probability of an event 7038 A conditional on an event B may strictly contain the bounds on the unconditional 7039 probability of A. Surprisingly, this might happen for every B in a partition 7040 \mathscr{B}. If so, we say that dilation has occurred. In addition to being an 7041 interesting statistical curiosity, this counterintuitive phenomenon has 7042 important implications in robust Bayesian inference and in the theory of upper 7043 and lower probabilities. We investigate conditions under which dilation occurs 7044 and we study some of its implications. We characterize dilation immune 7045 neighborhoods of the uniform measure.}, 7046 annote = {ook op papier}, 7047 author = {Teddy Seidenfeld and Larry Wasserman}, 7048 doi = {10.1214/aos}, 7049 journal = {The Annals of Statistics}, 7050 localfile = {article/Seidenfeld-Wasserman-1993.pdf}, 7051 number = {3}, 7052 pages = {1139–1154}, 7053 publisher = {Institute of Mathematical Statistics}, 7054 title = {Dilation for sets of probabilities}, 7055 volume = {21}, 7056 year = {1993} 7057 } 7058 7059 @article{Giron-Rios-1980, 7060 abstract = {In this paper the theoretical and practical implications of 7061 dropping-from the basic Bayesian coherence principles- the assumption of 7062 comparability of every pair of acts is examined. The resulting theory is shown 7063 to be still perfectly coherent and has Bayesian theory as a particular case. In 7064 particular we question the need of weakening or ruling out some of the axioms 7065 that constitute the coherence principles; what are their practical implications; 7066 how this drive to the notion of partial information or partial uncertainty in a 7067 certain sense; how this partial information is combined with sample information 7068 and how this relates to Bayesian methods. We also point out the relation of this 7069 approach to rational behaviour with the more (and apparently unrelated) general 7070 notion of domination structures as applied to multicrieria decision making.}, 7071 author = {F. J. Girón and S. Rios}, 7072 doi = {10.1007/BF02888345}, 7073 journal = {Trabajos de Estadística y de Investigación Operativa}, 7074 localfile = {article/Giron-Rios-1980.pdf}, 7075 number = {1}, 7076 pages = {17–38}, 7077 title = {Quasi-Bayesian behaviour: a more realistic approach to decision making?}, 7078 volume = {31}, 7079 year = {1980} 7080 } 7081 7082 @book{Grunbaum-1967, 7083 address = {London}, 7084 author = {Branko Grünbaum}, 7085 publisher = {Interscience Publishers}, 7086 title = {Convex Polytopes}, 7087 year = {1967} 7088 } 7089 7090 @article{Sine-1990-Perron-Frobenius, 7091 abstract = {If T is a nonexpansive map on a domain in a 7092 finite-dimensional sup-norm space then there is a universal bound on the periods 7093 of periodic points. This yields the same result for T nonexpansive on a domain 7094 in a finite-dimensional Banach space which has a polyhedral unit ball. Similar 7095 results are obtained for certain nonexpansive maps defined on all of an 7096 infinite-dimensional L\_p space with 1<p<∞.}, 7097 author = {Robert Sine}, 7098 journal = {Proceedings of the American Mathematical Society}, 7099 localfile = {article/Sine-1990-Perron-Frobenius.pdf}, 7100 number = {2}, 7101 pages = {331–336}, 7102 title = {A nonlinear Perron-Frobenius theorem}, 7103 url = {http://www.ams.org/proc/1990-109-02/S0002-9939-1990-0948156-X/S0002-9939-1990-0 7104 948156-X.pdf}, 7105 volume = {109}, 7106 year = {1990} 7107 } 7108 7109 @article{Skyrms-1993, 7110 abstract = {Maher (1992b) advances an objection to dynamic Dutch-book 7111 arguments, partly inspired by the discussion in Levi (1987; in particular by 7112 Levi's case 2, p. 204). Informally, the objection is that the decision maker 7113 will "see the dutch book coming" and consequently refuse to bet, thus escaping 7114 the Dutch book. Maher makes this explicit by modeling the decision maker's 7115 choices as a sequential decision problem. On this basis he claims that there is 7116 a mistake in dynamic coherence arguments. There is really no formal mistake in 7117 classical dynamic coherence arguments, but the discussions in Maher and Levi do 7118 suggest interesting ways in which the definition of dynamic coherence might be 7119 strengthened. Such a strengthened "sequentialized" notion of dynamic coherence 7120 is explored here. It so happens that even on the strengthened standards for a 7121 Dutch book, the classic dynamic coherence argument for conditioning still goes 7122 through.}, 7123 author = {Brian Skyrms}, 7124 issn = {0031-8248}, 7125 journal = {Philosophy of Science}, 7126 localfile = {article/Skyrms-1993.pdf}, 7127 number = {2}, 7128 pages = {320–328}, 7129 publisher = {The University of Chicago Press on behalf of the Philosophy of Science Association}, 7130 title = {A mistake in dynamic coherence arguments?}, 7131 url = {http://www.jstor.org/stable/188357}, 7132 volume = {60}, 7133 year = {1993} 7134 } 7135 7136 @book{Brown-1986, 7137 address = {Hayward, California}, 7138 annote = {Geselecteerde delen kopies}, 7139 author = {Lawrence D. Brown}, 7140 editor = {Shanti S. Gupta}, 7141 publisher = {Institute of Mathematical Statistics}, 7142 series = {Institute of Mathematical Statistics: Lecture Notes—Monograph Series}, 7143 title = {Fundamentals of Statistical Exponential Families (with Applications in Statistical Decision Theory)}, 7144 volume = {9}, 7145 year = {1986} 7146 } 7147 7148 @inproceedings{Feron-1981, 7149 address = {New York}, 7150 annote = {Proceedings of the International Congress on Applied Systems Research and Cybernetics, Acapulco, Mexico, December 1980 enkel op papier}, 7151 author = {R. Feron}, 7152 booktitle = {Applied Systems and Cybernetics}, 7153 editor = {G. E. Lasker}, 7154 pages = {2831–2836}, 7155 publisher = {Pergamom Press}, 7156 series = {Fuzzy Sets and Systems, Possibility Theory and Special Topics in Systems Research}, 7157 title = {Probabilistic and statistical study of random fuzzy sets whose referential is R^N}, 7158 volume = {VI}, 7159 year = {1981} 7160 } 7161 7162 @inproceedings{Baroni-Vicig-2000-interchange, 7163 author = {Pietro Baroni and Paolo Vicig}, 7164 booktitle = {Proceedings of IPMU 2000}, 7165 pages = {1027–1034}, 7166 title = {An uncertainty interchange format for multi-agent systems based on imprecise probabilities}, 7167 year = {2000} 7168 } 7169 7170 @article{Fudenberg-Levine-1995, 7171 abstract = {We study a variation of fictitious play, in which the 7172 probability of each action is an exponential function of that action's utility 7173 against the historical frequency of opponents' play. Regardless of the 7174 opponents' strategies, the utility received by an agent using this rule is 7175 nearly the best that could be achieved against the historical frequency. Such 7176 rules are approximately optimal in i.i.d. environments, and guarantee nearly the 7177 minmax regardless of opponents' behavior. Fictitious play shares these 7178 properties provided it switches ‘infrequently’ between actions. We also study 7179 the long-run outcomes when all players use consistent and cautious rules.}, 7180 author = {Drew Fudenberg and David K. Levine}, 7181 doi = {10.1016/0165-1889(94)00819-4}, 7182 journal = {Journal of Economic Dynamics and Control}, 7183 keywords = {Games; Learning; Rationality; consistency}, 7184 localfile = {article/Fudenberg-Levine-1995.pdf}, 7185 number = {5-7}, 7186 pages = {1065–1089}, 7187 publisher = {Elsevier}, 7188 title = {Consistency and cautious fictitious play}, 7189 volume = {19}, 7190 year = {1995} 7191 } 7192 7193 @article{DeFinetti-1937, 7194 annote = {geannoteerde kopie}, 7195 author = {Bruno de Finetti}, 7196 journal = {Annales de l'Institut Henri Poincaré}, 7197 localfile = {article/DeFinetti-1937.pdf}, 7198 number = {1}, 7199 pages = {1–68}, 7200 publisher = {Institut Henri Poincaré}, 7201 title = {La prévision: ses lois logiques, ses sources subjectives}, 7202 url = {http://www.numdam.org/item?id=AIHP_1937__7_1_1_0}, 7203 volume = {7}, 7204 year = {1937} 7205 } 7206 7207 @article{Arnold-Castillo-Sarabia-1993, 7208 annote = {ook op papier}, 7209 author = {Barry C. Arnold and Enrique Castillo and Jose María Sarabia}, 7210 doi = {10.1080/02331889308802432}, 7211 journal = {Statistics}, 7212 localfile = {article/Arnold-Castillo-Sarabia-1993.pdf}, 7213 pages = {71–77}, 7214 publisher = {Taylor \& Francis}, 7215 title = {Conjugate exponential family priors for exponential family likelihoods}, 7216 volume = {25}, 7217 year = {1993} 7218 } 7219 7220 @inproceedings{Schervish-Seidenfeld-Kadane-2003-incoherence, 7221 address = {Oxford}, 7222 annote = {Proceedings of the Seventh Valencia International Meeting, 2–6 June 2002}, 7223 author = {Mark J. Schervish and Teddy Seidenfeld and Joseph B. Kadane}, 7224 booktitle = {Bayesian Statistics 7}, 7225 editor = {José M. Bernardo and others}, 7226 organization = {ISBA}, 7227 pages = {385–402}, 7228 publisher = {Clarendon Press}, 7229 title = {Measures of incoherence: How not to gamble if you must}, 7230 year = {2003} 7231 } 7232 7233 @article{Levi-1977, 7234 author = {Isaac Levi}, 7235 journal = {The Journal of Philosophy}, 7236 localfile = {article/Levi-1977.pdf}, 7237 number = {1}, 7238 pages = {5–29}, 7239 title = {Direct inference}, 7240 url = {http://www.jstor.org/stable/2025732}, 7241 volume = {74}, 7242 year = {1977} 7243 } 7244 7245 @article{Mosimann-1962, 7246 annote = {ook op papier}, 7247 author = {James E. Mosimann}, 7248 journal = {Biometrika}, 7249 localfile = {article/Mosimann-1962.pdf}, 7250 number = {1/2}, 7251 pages = {65–82}, 7252 title = {On the compound multinomial distribution, the multivariate $\beta$-distribution, and correlations among proportions}, 7253 url = {http://www.jstor.org/stable/2333468}, 7254 volume = {49}, 7255 year = {1962} 7256 } 7257 7258 @article{Diaconis-Freedman-1982-exchangeability, 7259 abstract = {Let X\_1, X\_2,⋯, X\_k, X\_{k+1},⋯, X\_n be exchangeable 7260 random variables taking values in the set S. The variation distance between the 7261 distribution of X\_1, X\_2,⋯, X\_k and the closest mixture of independent, 7262 identically distributed random variables is shown to be at most 2 ck/n, where c 7263 is the cardinality of S. If c is infinite, the bound k(k - 1)/n is obtained. 7264 These results imply the most general known forms of de Finetti's theorem. 7265 Examples are given to show that the rates k/n and k(k - 1)/n cannot be improved. 7266 The main tool is a bound on the variation distance between sampling with and 7267 without replacement. For instance, suppose an urn contains n balls, each marked 7268 with some element of the set S, whose cardinality c is finite. Now k draws are 7269 made at random from this urn, either with or without replacement. This generates 7270 two probability distributions on the set of k-tuples, and the variation distance 7271 between them is at most 2 ck/n.}, 7272 author = {Persi Diaconis and D. Freedman}, 7273 journal = {The Annals of Probability}, 7274 localfile = {article/Diaconis-Freedman-1982-exchangeability.pdf}, 7275 number = {4}, 7276 pages = {745–764}, 7277 title = {Finite exchangeable sequences}, 7278 url = {http://www.jstor.org/stable/2242823}, 7279 volume = {8}, 7280 year = {1980} 7281 } 7282 7283 @book{Durbin-etal-1998-seqalign, 7284 author = {R. Durbin and S. R. Eddy and Anders Krogh and G. Mitchison}, 7285 publisher = {Cambridge University Press}, 7286 title = {Biological sequence analysis: probabilistic models of proteins and nucleic acids}, 7287 year = {1998} 7288 } 7289 7290 @article{Coolen-1993, 7291 abstract = {Reconsidering generalizations of the original Bayesian 7292 framework that have been suggested during the last three decades, imprecise 7293 conjugate prior densities are proposed for members of the one-parameter 7294 exponential family of distributions.}, 7295 annote = {reprint}, 7296 author = {Frank P. A. Coolen}, 7297 doi = {10.1016/0167-7152(93)90066-R}, 7298 journal = {Statistics \& Probability Letters}, 7299 keywords = {Bayesian theory; conjugate priors; imprecise pro}, 7300 localfile = {article/Coolen-1993.pdf}, 7301 number = {5}, 7302 pages = {337–342}, 7303 publisher = {Elsevier}, 7304 title = {Imprecise conjugate prior densities for the one-parameter exponential family of distributions}, 7305 volume = {16}, 7306 year = {1993} 7307 } 7308 7309 @article{Campos-Cozman-2007-epistemic, 7310 abstract = {This paper investigates the computation of lower/upper 7311 expectations that must cohere with a collection of probabilistic assessments and 7312 a collection of judgements of epistemic independence. New algorithms, based on 7313 multilinear programming, are presented, both for independence among events and 7314 among random variables. Separation properties of graphical models are also 7315 investigated.}, 7316 author = {Cassio Polpo de Campos and Fabio Gagliardi Cozman}, 7317 doi = {10.1016/j.ijar.2006.07.013}, 7318 issn = {0888-613X}, 7319 journal = {International Journal of Approximate Reasoning}, 7320 keywords = {concepts of independence; epistemic independence; imprecise probabilities; multilinear programming; sets of probability measures}, 7321 localfile = {article/Campos-Cozman-2007-epistemic.pdf}, 7322 number = {3}, 7323 pages = {244–260}, 7324 publisher = {Elsevier}, 7325 title = {Computing lower and upper expectations under epistemic independence}, 7326 url = {http://www.sciencedirect.com/science/article/pii/S0888613X0600096X}, 7327 volume = {44}, 7328 year = {2007} 7329 } 7330 7331 @article{Kreinovich-Xiang-Ferson-2006, 7332 abstract = {In many real-life situations, we only have partial 7333 information about the actual probability distribution. For example, under 7334 Dempster-Shafer uncertainty, we only know the masses m1, ... ,mn assigned to 7335 different sets S1, ... ,Sn, but we do not know the distribution within each set 7336 Si. Because of this uncertainty, there are many possible probability 7337 distributions consistent with our knowledge; different distributions have, in 7338 general, different values of standard statistical characteristics such as mean 7339 and variance. It is therefore desirable, given a Dempster-Shafer knowledge base, 7340 to compute the ranges and of possible values of mean E and of variance V. In 7341 their recent paper, Langewisch and Choobineh show how to compute these ranges in 7342 polynomial time. In particular, they reduce the problem of computing to the 7343 problem of minimizing a convex quadratic function, a problem which can be solved 7344 in time O(n2 [middle dot] log(n)). We show that the corresponding quadratic 7345 optimization problem can be actually solved faster, in time O(n [middle dot] 7346 log(n)); thus, we can compute the bounds V and in time O(n [middle dot] 7347 log(n)).}, 7348 author = {Vladik Kreinovich and Gang Xiang and Scott Ferson}, 7349 doi = {10.1016/j.ijar.2005.12.001}, 7350 journal = {International Journal of Approximate Reasoning}, 7351 localfile = {article/Kreinovich-Xiang-Ferson-2006.pdf}, 7352 number = {3}, 7353 pages = {212–227}, 7354 title = {Computing mean and variance under Dempster-Shafer uncertainty: Towards faster algorithms}, 7355 volume = {42}, 7356 year = {2006} 7357 } 7358 7359 @article{Inuiguchi-2007, 7360 abstract = {In this paper, we treat fuzzy linear programming problems 7361 with uncertain parameters whose ranges are specified as fuzzy polytopes. The 7362 problem is formulated as a necessity measure optimization model. It is shown 7363 that the problem can be reduced to a semi-infinite programming problem and 7364 solved by a combination of a bisection method and a relaxation procedure. An 7365 algorithm in which the bisection method and the relaxation procedure converge 7366 simultaneously is proposed. A simple numerical example is given to illustrate 7367 the solution procedure.}, 7368 author = {Masahiro Inuiguchi}, 7369 doi = {10.1016/j.fss.2007.04.004}, 7370 issn = {0165-0114}, 7371 journal = {Fuzzy Sets and Systems}, 7372 keywords = {Bisection method; Fuzzy polytope; Necessity measure; Possibilistic linear programming; Relaxation procedure; Semi-infinite programming}, 7373 localfile = {article/Inuiguchi-2007.pdf}, 7374 number = {17}, 7375 pages = {1882–1891}, 7376 title = {Necessity measure optimization in linear programming problems with fuzzy polytopes}, 7377 volume = {158}, 7378 year = {2007} 7379 } 7380 7381 @book{Letac-1992, 7382 annote = {Hoofdstukken 1, 2 en 4 kopies}, 7383 author = {Gérard Letac}, 7384 number = {50}, 7385 publisher = {Conselho Nacional de Desenvolvimento Cientifico e Tecnológico, Instituto de Matemática Pura e Aplicada (IMPA)}, 7386 series = {Monografias de Matemática}, 7387 title = {Lectures on natural exponential families and their variance functions}, 7388 year = {1992} 7389 } 7390 7391 @article{Tanaka-1993, 7392 author = {Yoshihiro Tanaka}, 7393 journal = {Economic Journal of Hokkaido University}, 7394 localfile = {article/Tanaka-1993.pdf}, 7395 pages = {159–166}, 7396 title = {On Convexity of A System of Linear Interval Equations}, 7397 url = {http://hdl.handle.net/2115/30499}, 7398 volume = {22}, 7399 year = {1993} 7400 } 7401 7402 @book{Whittle-1992, 7403 author = {Peter Whittle}, 7404 edition = {3}, 7405 series = {Springer Texts in Statistics}, 7406 title = {Probability via Expectation}, 7407 volume = {XVIII}, 7408 year = {1992} 7409 } 7410 7411 @proceedings{SMPS-2004, 7412 address = {Oviedo, Spain}, 7413 booktitle = {Soft Methodology and Random Information Systems}, 7414 editor = {Miguel Lopéz-Díaz and María Angeles Gil and Przemysław Grzegorzewski and Olgierd Hryniewicz and Jonathan Lawry}, 7415 publisher = {Springer}, 7416 series = {Advances in soft computing}, 7417 title = {Soft Methodology and Random Information Systems}, 7418 year = {2004} 7419 } 7420 7421 @article{DeCooman-Miranda-Quaeghebeur-2009-RIP, 7422 abstract = {We consider immediate predictive inference, where a subject, 7423 using a number of observations of a finite number of exchangeable random 7424 variables, is asked to coherently model his beliefs about the next observation, 7425 in terms of a predictive lower prevision. We study when such predictive lower 7426 previsions are representation insensitive, meaning that they are essentially 7427 independent of the choice of the (finite) set of possible values for the random 7428 variables. We establish that such representation insensitive predictive models 7429 have very interesting properties, and show that among such models, the ones 7430 produced by the Imprecise Dirichlet-Multinomial Model are quite special in a 7431 number of ways. In the Conclusion, we discuss the open question as to how unique 7432 the predictive lower previsions of the Imprecise Dirichlet-Multinomial Model are 7433 in being representation insensitive.}, 7434 author = {Gert {De Cooman} and Enrique Miranda and Erik Quaeghebeur}, 7435 doi = {10.1016/j.ijar.2008.03.010}, 7436 issn = {0888-613X}, 7437 journal = {International Journal of Approximate Reasoning}, 7438 keywords = {Coherence; Exchangeability; Immediate prediction; Imprecise Dirichlet-Multinomial Model; Imprecise probabilities; Johnson’s sufficientness postulate; Lower prevision; Predictive inference; Representation insensitivity; Representation invariance principle; Rule of Succession}, 7439 localfile = {article/DeCooman-Miranda-Quaeghebeur-2009-RIP.pdf}, 7440 number = {2}, 7441 pages = {204–216}, 7442 publisher = {Elsevier}, 7443 title = {Representation insensitivity in immediate prediction under exchangeability}, 7444 volume = {50}, 7445 year = {2009} 7446 } 7447 7448 @book{Boyd-Vandenberghe-2004, 7449 author = {Stephen Boyd and Lieven Vandenberghe}, 7450 publisher = {Cambridge University Press}, 7451 title = {Convex Optimization}, 7452 url = {http://www.stanford.edu/~boyd/cvxbook}, 7453 year = {2004} 7454 } 7455 7456 @book{Golub-VanLoan-1989, 7457 author = {Gene H. Golub and Charles F. {Van Loan}}, 7458 edition = {2}, 7459 publisher = {Johns Hopkins University Press}, 7460 series = {Johns Hopkins Series in the Mathematical Sciences}, 7461 title = {Matrix Computation}, 7462 year = {1989} 7463 } 7464 7465 @article{Shapley-1971, 7466 abstract = {The core of an n-person game is the set of feasible outcomes 7467 that cannot be improved upon by any coalition of players. A convex game is 7468 defined as one that is based on a convex set function. In this paper it is shown 7469 that the core of a convex game is not empty and that it has an especially 7470 regular structure. It is further shown that certain other cooperative solution 7471 concepts are related in a simple way to the core: The value of a convex game is 7472 the center of gravity of the extreme points of the core, and the von 7473 Neumann-Morgenstern stable set solution of a convex game is unique and coincides 7474 with the core.}, 7475 annote = {ook op papier}, 7476 author = {Lloyd S. Shapley}, 7477 doi = {10.1007/BF01753431}, 7478 journal = {International Journal of Game Theory}, 7479 localfile = {article/Shapley-1971.pdf}, 7480 number = {1}, 7481 pages = {11–26}, 7482 publisher = {Springer}, 7483 title = {Cores of convex games}, 7484 volume = {1}, 7485 year = {1971} 7486 } 7487 7488 @article{Nowak-May-Sigmund-1995connor, 7489 author = {Martin A. Nowak and Robert M. May and Karl Sigmund}, 7490 journal = {Scientific American}, 7491 pages = {76–81}, 7492 title = {The Arithmetics of Mutual Help}, 7493 year = {1995} 7494 } 7495 7496 @article{Frechet-1948, 7497 author = {Maurice Fréchet}, 7498 journal = {Annales de l'Institut Henri Poincaré}, 7499 localfile = {article/Frechet-1948.pdf}, 7500 number = {4}, 7501 pages = {215–310}, 7502 title = {Les éléments aléatoires de nature quelconque dans un espace distancié}, 7503 url = {http://www.numdam.org/item?id=AIHP_1948__10_4_215_0}, 7504 volume = {10}, 7505 year = {1948} 7506 } 7507 7508 @proceedings{NIPS2003, 7509 booktitle = {NIPS}, 7510 editor = {Sebastian Thrun and Lawrence K Saul and Bernhard Schölkopf}, 7511 isbn = {0-262-20152-6}, 7512 publisher = {MIT Press}, 7513 title = {Advances in Neural Information Processing Systems 16 [Neural Information Processing Systems, NIPS 2003, December 8-13, 2003, Vancouver and Whistler, British Columbia, Canada]}, 7514 year = {2004} 7515 } 7516 7517 @proceedings{ICML-2000, 7518 booktitle = {Proceedings of the 17th International Conference on Machine Learning (ICML-2000)}, 7519 title = {Proceedings of the 17th International Conference on Machine Learning (ICML-2000)}, 7520 year = {2000} 7521 } 7522 7523 @inproceedings{Williams-1975-coherence, 7524 author = {Peter M. Williams}, 7525 booktitle = {Fifth International Congress of Logic, Methodology and Philosophy of Science}, 7526 pages = {29–33}, 7527 title = {Coherence, strict coherence and zero probabilities}, 7528 volume = {VI}, 7529 year = {1975} 7530 } 7531 7532 @article{Miranda-2008-survey, 7533 abstract = {This paper presents a summary of Peter Walley's theory of 7534 coherent lower previsions. We introduce three representations of coherent 7535 assessments: coherent lower and upper previsions, closed and convex sets of 7536 linear previsions, and sets of desirable gambles. We show also how the notion of 7537 coherence can be used to update our beliefs with new information, and a number 7538 of possibilities to model the notion of independence with coherent lower 7539 previsions. Next, we comment on the connection with other approaches in the 7540 literature: de Finetti's and Williams' earlier work, Kuznetsov's and 7541 Weischelberger's work on interval-valued probabilities, Dempster-Shafer theory 7542 of evidence and Shafer and Vovk's game-theoretic approach. Finally, we present a 7543 brief survey of some applications and summarize the main strengths and 7544 challenges of the theory.}, 7545 author = {Enrique Miranda}, 7546 doi = {10.1016/j.ijar.2007.12.001}, 7547 journal = {International Journal of Approximate Reasoning}, 7548 keywords = {Avoiding sure loss; Coherence; Conditional lower previsions; Desirability; Imprecision; Independence; Subjective probability}, 7549 localfile = {article/Miranda-2008-survey.pdf}, 7550 number = {2}, 7551 pages = {628–658}, 7552 title = {A survey of the theory of coherent lower previsions}, 7553 volume = {48}, 7554 year = {2008} 7555 } 7556 7557 @book{Munro-1999, 7558 editor = {N. Munro}, 7559 publisher = {The Institution of Electrical Engineers (IEE)}, 7560 title = {The Use of Symbolic Methods in Control System Analysis and Design}, 7561 year = {1999} 7562 } 7563 7564 @book{Mura-2008, 7565 author = {Bruno de Finetti}, 7566 doi = {10.1007/978-1-4020-8202-3}, 7567 editor = {Alberto Mura}, 7568 publisher = {Springer}, 7569 series = {Synthese Library}, 7570 title = {Philosophical Lectures on Probability}, 7571 volume = {340}, 7572 year = {2008} 7573 } 7574 7575 @article{DeCooman-Hermans-Quaeghebeur-2009-PES, 7576 author = {Gert {De Cooman} and Filip Hermans and Erik Quaeghebeur}, 7577 doi = {10.1017/S0269964809990039}, 7578 journal = {Probability in the Engineering and Informational Sciences}, 7579 number = {4}, 7580 pages = {597–635}, 7581 title = {Imprecise Markov chains and their limit behavior}, 7582 volume = {23}, 7583 year = {2009} 7584 } 7585 7586 @book{Keynes-1921, 7587 author = {John Maynard Keynes}, 7588 publisher = {Macmillan}, 7589 title = {A Treatise on Probability}, 7590 url = {http://www.gutenberg.org/ebooks/32625}, 7591 year = {1921} 7592 } 7593 7594 @article{Moslehian-2006, 7595 archiveprefix = {arXiv}, 7596 arxivid = {math/0501048}, 7597 author = {Mohammad Sal Moslehian}, 7598 eprint = {0501048}, 7599 journal = {Trends in Mathematics}, 7600 keywords = {Complemented subspace; L1-predual space; Schauder basis; basis; complementary minimal subspace; prime space; quasi-complemented subspace; sequence spaces; weakly complemented subspace}, 7601 localfile = {article/Moslehian-2006.pdf}, 7602 number = {1}, 7603 pages = {91–98}, 7604 primaryclass = {math}, 7605 title = {A survey of the complemented subspace problem}, 7606 volume = {9}, 7607 year = {2006} 7608 } 7609 7610 @book{Martin-1966, 7611 author = {J. J. Martin}, 7612 editor = {David B. Hertz}, 7613 number = {13}, 7614 publisher = {Wiley}, 7615 series = {Publications in Operations Research}, 7616 title = {Bayesian Decision problems and Markov Chains}, 7617 year = {1966} 7618 } 7619 7620 @article{Walley-Gurrin-Burton-1996, 7621 abstract = {This paper describes a new method, based on the theory of 7622 imprecise probabilities, for analysing clinical data in the form of a 7623 contingency table. The method is applied to a well-known set of statistical data 7624 from randomized clinical trials of two treatments for severe cardiorespiratory 7625 failure in newborn babies. Two problems are distinguished. The inference problem 7626 is to draw conclusions about which treatment is more effective. The decision 7627 problem is to determine whether one treatment should be preferred to another for 7628 the next patient, or whether it is ethical to select the treatment by 7629 randomization. The two problems are analysed using three possible models for 7630 prior ignorance about the statistical parameters, and one of the models is 7631 modified to take account of earlier clinical data. In this example the four 7632 models produce essentially the same conclusions.}, 7633 annote = {ook op papier}, 7634 author = {Peter Walley and Lyle Gurrin and Paul Burton}, 7635 journal = {The Statistician}, 7636 localfile = {article/Walley-Gurrin-Burton-1996.pdf}, 7637 number = {4}, 7638 pages = {457–485}, 7639 title = {Analysis of clinical data using imprecise prior probabilities}, 7640 url = {http://www.jstor.org/stable/2988546}, 7641 volume = {45}, 7642 year = {1996} 7643 } 7644 7645 @inproceedings{DeCooman-etal-ISIPTA09-Markovtrees, 7646 abstract = {We replace strong independence in credal networks with the 7647 weaker notion of epistemic irrelevance. Focusing on directed trees, we show how 7648 to combine local credal sets into a global model, and we use this to construct 7649 and justify an exact message-passing algorithm that computes updated beliefs for 7650 a variable in the tree. The algorithm, which is essentially linear in the number 7651 of nodes, is formulated entirely in terms of coherent lower previsions. We 7652 supply examples of the algorithm's operation, and report an application to 7653 on-line character recognition that illustrates the advantages of our model for 7654 prediction.}, 7655 address = {Durham, United Kingdom}, 7656 annote = {ook op papier}, 7657 author = {Gert {De Cooman} and Filip Hermans and Alessandro Antonucci and Marco Zaffalon}, 7658 booktitle = {ISIPTA '09: Proceedings of the Sixth International Symposium on Imprecise Probabilities: Theories and Applications}, 7659 editor = {Thomas Augustin and Frank P. A. Coolen and Serafin Moral and Matthias C. M. Troffaes}, 7660 organization = {SIPTA}, 7661 pages = {149–158}, 7662 title = {Epistemic irrelevance in credal networks: the case of imprecise Markov trees}, 7663 year = {2009} 7664 } 7665 7666 @inproceedings{Maass-2003-ISIPTA, 7667 address = {Waterloo, Ontario, Canada}, 7668 author = {Sebastian Maaß}, 7669 booktitle = {ISIPTA '03: Proceedings of the Third International Symposium on Imprecise Probabilities and Their Applications}, 7670 editor = {Jean-Marc Bernard and Teddy Seidenfeld and Marco Zaffalon}, 7671 location = {Lugano, Switzerland}, 7672 pages = {372–382}, 7673 publisher = {Carleton Scientific}, 7674 series = {Proceedings in Informatics}, 7675 title = {Continuous Linear Representations of Coherent Lower Previsions}, 7676 volume = {18}, 7677 year = {2003} 7678 } 7679 7680 @article{Miranda-DeCooman-2003, 7681 abstract = {Numerical possibility measures can be interpreted as systems 7682 of upper betting rates for events. As such, they have a special part in the 7683 unifying behavioural theory of imprecise probabilities, proposed by Walley. On 7684 this interpretation, they should arguably satisfy certain rationality, or 7685 consistency, requirements, such as avoiding sure loss and coherence. Using a 7686 version of Walley's notion of epistemic independence suitable for possibility 7687 measures, we study in detail what these rationality requirements tell us about 7688 the construction of independent product possibility measures from given 7689 marginals, and we obtain necessary and sufficient conditions for a product to 7690 satisfy these criteria. In particular, we show that the well-known minimum and 7691 product rules for forming independent joint distributions from marginal ones, 7692 are only coherent when at least one of these distributions assume just the 7693 values zero and one.}, 7694 annote = {reprint}, 7695 author = {Enrique Miranda and Gert {De Cooman}}, 7696 doi = {10.1016/S0888-613X(02)00087-7}, 7697 journal = {International Journal of Approximate Reasoning}, 7698 keywords = {Coherence; Conditioning; Epistemic independence; Independent product; Possibility theory; Upper probability}, 7699 localfile = {article/Miranda-DeCooman-2003.pdf}, 7700 pages = {23–42}, 7701 title = {Epistemic independence in numerical possibility theory}, 7702 volume = {32}, 7703 year = {2003} 7704 } 7705 7706 @article{Dawid-1985-symmetry, 7707 author = {A. Philip Dawid}, 7708 doi = {10.1093/bjps}, 7709 journal = {The British Journal for the Philosophy of Science}, 7710 localfile = {article/Dawid-1985-symmetry.pdf}, 7711 number = {2}, 7712 pages = {107–128}, 7713 publisher = {British Society for the Philosophy of Science}, 7714 title = {Probability, symmetry and frequency}, 7715 volume = {36}, 7716 year = {1985} 7717 } 7718 7719 @article{Consonni-Veronese-1992, 7720 annote = {ook op papier}, 7721 author = {Guido Consonni and Piero Veronese}, 7722 journal = {Journal of the American Statistical Association}, 7723 keywords = {Bayesian statistics; least favorable prior; partial prior information}, 7724 localfile = {article/Consonni-Veronese-1992.pdf}, 7725 number = {420}, 7726 pages = {1123–1127}, 7727 title = {Conjugate priors for exponential families having quadratic variance functions}, 7728 url = {http://www.jstor.org/stable/2290650}, 7729 volume = {87}, 7730 year = {1992} 7731 } 7732 7733 @article{GutierrezPena-Rueda-2003, 7734 abstract = {Reference analysis, introduced by Bernardo (J. Roy. Statist. 7735 Soc. 41 (1979) 113) and further developed by Berger and Bernardo (On the 7736 development of reference priors (with discussion). In: J.M. Bernardo, J.O. 7737 Berger, A.P. Dawid, A.F.M. Smith (Eds.), Bayesian Statistics, Vol. 4, Clarendon 7738 Press, Oxford, pp. 35-60), has proved to be one of the most successful general 7739 methods to derive noninformative prior distributions. In practice, however, 7740 reference priors are typically difficult to obtain. In this paper we show how to 7741 find reference priors for a wide class of exponential family likelihoods.}, 7742 author = {Eduardo Gutiérrez-Peña and R. Rueda}, 7743 doi = {10.1016/S0378-3758(01)00281-6}, 7744 journal = {Journal of Statistical Planning and Inference}, 7745 keywords = {Affine dual foliations; Bayesian inference; Natural exponential family; Quadratic variance function; Reference prior; cut}, 7746 localfile = {article/GutierrezPena-Rueda-2003.pdf}, 7747 number = {1-2}, 7748 pages = {35–54}, 7749 title = {Reference priors for exponential families}, 7750 volume = {110}, 7751 year = {2003} 7752 } 7753 7754 @inproceedings{Troffaes-2004, 7755 author = {Matthias C. M. Troffaes}, 7756 booktitle = {Proceedings of the Tenth International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems: IPMU 2004}, 7757 pages = {571–578}, 7758 title = {Efficient and robust global amino acid sequence alignment with uncertain evolutionary distances}, 7759 volume = {1}, 7760 year = {2004} 7761 } 7762 7763 @article{Bernard-1997-specificity, 7764 annote = {ook op papier}, 7765 author = {Jean-Marc Bernard}, 7766 journal = {Revue Internationale de Systémique}, 7767 localfile = {article/Bernard-1997-specificity.pdf}, 7768 number = {1}, 7769 pages = {11–29}, 7770 title = {Bayesian analysis of tree-structured data}, 7771 volume = {11}, 7772 year = {1997} 7773 } 7774 7775 @inbook{Boute-2004, 7776 annote = {Op papier}, 7777 author = {Raymond T. Boute}, 7778 booktitle = {Information Technology}, 7779 pages = {85–114}, 7780 publisher = {Kluwer Academic Publishers}, 7781 title = {Formal Reasoning about Systems, Software and Hardware using Functionals, Predicates and Relations}, 7782 year = {2004} 7783 } 7784 7785 @phdthesis{DeMunck-2009-PhD, 7786 author = {Maarten {De Munck}}, 7787 month = apr, 7788 school = {Katholieke Universiteit Leuven}, 7789 title = {Efficient optimization approaches for interval and fuzzy finite element analysis}, 7790 year = {2009} 7791 } 7792 7793 @book{Liu-2007-uncertain-programming, 7794 author = {Baoding Liu}, 7795 edition = {2}, 7796 title = {Theory and Practice of Uncertain Programming}, 7797 year = {2007} 7798 } 7799 7800 @article{Kubis-2002, 7801 abstract = {The purpose of this paper is to investigate some separation 7802 properties of sets with axiomatically defined convexity structures. We state a 7803 general separation theorem for pairs of convexities, improving some known 7804 results. As an application, we discuss separation properties of lattices, real 7805 vector spaces and modules.}, 7806 address = {Basel}, 7807 author = {Wiesław Kubiś}, 7808 doi = {10.1007/PL00012529}, 7809 issn = {0047-2468}, 7810 journal = {Journal of Geometry}, 7811 keywords = {Mathematics; Statistics}, 7812 localfile = {article/Kubis-2002.pdf}, 7813 number = {1}, 7814 pages = {110–119}, 7815 publisher = {Birkhäuser}, 7816 title = {Separation properties of convexity spaces}, 7817 volume = {74}, 7818 year = {2002} 7819 } 7820 7821 @article{Pelessoni-Vicig-2005-convex, 7822 abstract = {Two classes of imprecise previsions, which we termed convex 7823 and centered convex previsions, are studied in this paper in a framework close 7824 to Walley's and Williams' theory of imprecise previsions. We show that convex 7825 previsions are related with a concept of convex natural extension, which is 7826 useful in correcting a large class of inconsistent imprecise probability 7827 assessments, characterised by a condition of avoiding unbounded sure loss. 7828 Convexity further provides a conceptual framework for some uncertainty models 7829 and devices, like unnormalised supremum preserving functions. Centered convex 7830 previsions are intermediate between coherent previsions and previsions avoiding 7831 sure loss, and their not requiring positive homogeneity is a relevant feature 7832 for potential applications. We discuss in particular their usage in (financial) 7833 risk measurement. In a final part we introduce convex imprecise previsions in a 7834 conditional environment and investigate their basic properties, showing how 7835 several of the preceding notions may be extended and the way the generalised 7836 Bayes rule applies.}, 7837 author = {Renato Pelessoni and Paolo Vicig}, 7838 doi = {10.1016/j.ijar.2004.10.007}, 7839 issn = {0888-613X}, 7840 journal = {International Journal of Approximate Reasoning}, 7841 keywords = {Convex conditional imprecise previsions; Convex imprecise previsions; Convex natural extension; Generalised Bayes rule; Risk measures}, 7842 localfile = {article/Pelessoni-Vicig-2005-convex.pdf}, 7843 number = {2-3}, 7844 pages = {297–319}, 7845 title = {Uncertainty modelling and conditioning with convex imprecise previsions}, 7846 volume = {39}, 7847 year = {2005} 7848 } 7849 7850 @article{Berger-1994-robust-overview, 7851 abstract = {Robust Bayesian analysis is the study of the sensitivity of 7852 Bayesian answers to uncertain inputs. This paper seeks to provide an overview of 7853 the subject, one that is accessible to statisticians outside the field. Recent 7854 developments in the area are also reviewed, though with very uneven emphasis.}, 7855 author = {James Berger and Elías Moreno and Luis Raúl Pericchi and M. Bayarri and José M. Bernardo and Juan Cano and Julián {De la Horra} and Jacinto Martín and David Ríos-Insúa and Bruno Betrò and A. Dasgupta and Paul Gustafson and Larry Wasserman and Joseph B. Kadane and Srinivasan Cid and Michael Lavine and Anthony O'Hagan and Wolfgang Polasek and Christian Robert and Constantinos Goutis and Fabrizio Ruggeri and Gabriella Salinetti and Siva Sivaganesan}, 7856 doi = {10.1007/BF02562676}, 7857 journal = {Test}, 7858 number = {1}, 7859 pages = {5–124}, 7860 title = {An overview of Robust Bayesian analysis}, 7861 volume = {3}, 7862 year = {1994} 7863 } 7864 7865 @book{Shafer-1976, 7866 author = {Glenn Shafer}, 7867 publisher = {Princeton University Press}, 7868 title = {A mathematical theory of evidence}, 7869 year = {1976} 7870 } 7871 7872 @article{Hsu-et-al-2005, 7873 abstract = {Much is known about how people make decisions under varying 7874 levels of probability (risk). Less is known about the neural basis of 7875 decision-making when probabilities are uncertain because of missing information 7876 (ambiguity). In decision theory, ambiguity about probabilities should not affect 7877 choices. Using functional brain imaging, we show that the level of ambiguity in 7878 choices correlates positively with activation in the amygdala and orbitofrontal 7879 cortex, and negatively with a striatal system. Moreover, striatal activity 7880 correlates positively with expected reward. Neurological subjects with 7881 orbitofrontal lesions were insensitive to the level of ambiguity and risk in 7882 behavioral choices. These data suggest a general neural circuit responding to 7883 degrees of uncertainty, contrary to decision theory.}, 7884 author = {Ming Hsu and Meghana Bhatt and Ralph Adolphs and Daniel Tranel and Colin F. Camerer}, 7885 doi = {10.1126/science.1115327}, 7886 journal = {Science}, 7887 localfile = {article/Hsu-et-al-2005.pdf}, 7888 month = dec, 7889 number = {5754}, 7890 pages = {1680–1683}, 7891 publisher = {American Association for the Advancement of Science}, 7892 title = {Neural systems responding to degrees of uncertainty in human decision-making}, 7893 volume = {310}, 7894 year = {2005} 7895 } 7896 7897 @phdthesis{Maass-2003-PhD, 7898 author = {Sebastian Maaß}, 7899 school = {Universität Bremen}, 7900 title = {Exact functionals, functionals preserving linear inequalities, Lévy's metric}, 7901 year = {2003} 7902 } 7903 7904 @article{Good-1952, 7905 abstract = {This paper deals first with the relationship between the 7906 theory of probability and the theory of rational behaviour. A method is then 7907 suggested for encouraging people to make accurate probability estimates, a 7908 connection with the theory of information being mentioned. Finally Wald's theory 7909 of statistical decision functions is summarised and generalised and its relation 7910 to the theory of rational behaviour is discussed.}, 7911 author = {I. J. Good}, 7912 issn = {0035-9246}, 7913 journal = {Journal of the Royal Statistical Society. Series B (Methodological)}, 7914 localfile = {article/Good-1952.pdf}, 7915 number = {1}, 7916 pages = {107–114}, 7917 publisher = {Blackwell Publishing for the Royal Statistical Society}, 7918 title = {Rational decisions}, 7919 url = {http://www.jstor.org/stable/2984087}, 7920 volume = {14}, 7921 year = {1952} 7922 } 7923 7924 @article{Sundberg-Wagner-1992, 7925 annote = {op papier in Wagnerbundel}, 7926 author = {Carl Sundberg and Carl G. Wagner}, 7927 journal = {Advances in Applied Mathematics of Operations Research}, 7928 pages = {262–272}, 7929 title = {Generalized Differences and Bayesian Conditioning of Choquet Capacities}, 7930 volume = {13}, 7931 year = {1992} 7932 } 7933 7934 @article{DeCooman-Aeyels-1999, 7935 abstract = {We study the relation between possibility measures and the 7936 theory of imprecise probabilities, and argue that possibility measures have an 7937 important part in this theory. It is shown that a possibility measure is a 7938 coherent upper probability if and only if it is normal. A detailed comparison is 7939 given between the possibilistic and natural extension of an upper probability, 7940 both in the general case and for upper probabilities defined on a class of 7941 nested sets. We prove in particular that a possibility measure is the 7942 restriction to events of the natural extension of a special kind of upper 7943 probability, defined on a class of nested sets. We show that possibilistic 7944 extension can be interpreted in terms of natural extension. We also prove that 7945 when either the upper or the lower cumulative distribution function of a random 7946 quantity is specified, possibility measures very naturally emerge as the 7947 corresponding natural extensions. Next, we go from upper probabilities to upper 7948 previsions. We show that if a coherent upper prevision defined on the convex 7949 cone of all non-negative gambles is supremum preserving, then it must take the 7950 form of a Shilkret integral associated with a possibility measure. But at the 7951 same time, we show that such a supremum preserving upper prevision is never 7952 coherent unless it is the vacuous upper prevision with respect to a non-empty 7953 subset of the universe of discourse.}, 7954 author = {Gert {De Cooman} and Dirk Aeyels}, 7955 doi = {10.1016/S0020-0255(99)00007-9}, 7956 issn = {0020-0255}, 7957 journal = {Information Sciences}, 7958 keywords = {choquet integral; coherence; lower cumulative distribution function; natural extension; possibilistic extension; possibility measure; upper cumulative distribution function; upper probability}, 7959 localfile = {article/DeCooman-Aeyels-1999.pdf}, 7960 number = {1-4}, 7961 pages = {173–212}, 7962 publisher = {Elsevier}, 7963 title = {Supremum preserving upper probabilities}, 7964 volume = {118}, 7965 year = {1999} 7966 } 7967 7968 @misc{Bernard-2003, 7969 annote = {Tutorial for ISIPTA'03}, 7970 author = {Jean-Marc Bernard}, 7971 title = {An Introduction to the Imprecise Dirichlet Model for Multinomial Data}, 7972 year = {2003} 7973 } 7974 7975 @misc{Doumont-2001-speaking, 7976 author = {Jean-luc Doumont}, 7977 title = {Speaking in public}, 7978 year = {2001} 7979 } 7980 7981 @book{Raiffa-Schlaifer-1961, 7982 address = {Cambridge, Massachusetts}, 7983 annote = {Boek bij René}, 7984 author = {Howard Raiffa and Robert Schlaifer}, 7985 publisher = {MIT Press}, 7986 title = {Applied Statistical decision Theory}, 7987 year = {1968} 7988 } 7989 7990 @article{Barabasi-Oltvai-2004, 7991 abstract = {A key aim of postgenomic biomedical research is to 7992 systematically catalogue all molecules and their interactions within a living 7993 cell. There is a clear need to understand how these molecules and the 7994 interactions between them determine the function of this enormously complex 7995 machinery, both in isolation and when surrounded by other cells. Rapid advances 7996 in network biology indicate that cellular networks are governed by universal 7997 laws and offer a new conceptual framework that could potentially revolutionize 7998 our view of biology and disease pathologies in the twenty-first century.}, 7999 annote = {ook op papier}, 8000 author = {Albert-László Barabási and Zoltán N. Oltvai}, 8001 doi = {10.1038/nrg1272}, 8002 journal = {Nature Reviews Genetics}, 8003 localfile = {article/Barabasi-Oltvai-2004.pdf}, 8004 number = {2}, 8005 pages = {101–113}, 8006 publisher = {Nature Publishing Group}, 8007 title = {Network biology: understanding the cell's functional organization}, 8008 volume = {5}, 8009 year = {2004} 8010 } 8011 8012 @article{Jordan-2004-graphical, 8013 author = {Michael I. Jordan}, 8014 doi = {10.1214/088342304000000026}, 8015 journal = {Statistical Science}, 8016 localfile = {article/Jordan-2004-graphical.pdf}, 8017 number = {1}, 8018 pages = {140–155}, 8019 title = {Graphical Models}, 8020 volume = {19}, 8021 year = {2004} 8022 } 8023 8024 @book{Johnson-Kemp-Kotz-2005, 8025 author = {Norman L. Johnson and Adrienne W. Kemp and Samuel Kotz}, 8026 edition = {3}, 8027 publisher = {Wiley}, 8028 title = {Univariate Discrete Distributions}, 8029 year = {2005} 8030 } 8031 8032 @article{DeCooman-Troffaes-Miranda-2008-exact, 8033 abstract = {We study n-monotone functionals, which constitute a 8034 generalisation of n-monotone set functions. We investigate their relation to the 8035 concepts of exactness and natural extension, which generalise coherence and 8036 natural extension in the behavioural theory of imprecise probabilities. We 8037 improve upon a number of results in the literature, and prove among other things 8038 a representation result for exact n-monotone functionals in terms of Choquet 8039 integrals.}, 8040 author = {Gert {De Cooman} and Matthias C. M. Troffaes and Enrique Miranda}, 8041 doi = {10.1016/j.jmaa.2008.05.071}, 8042 issn = {0022-247X}, 8043 journal = {Journal of Mathematical Analysis and Applications}, 8044 keywords = {Choquet integral; coherence; comonotone additivi}, 8045 localfile = {article/DeCooman-Troffaes-Miranda-2008-exact.pdf}, 8046 number = {1}, 8047 pages = {143–156}, 8048 publisher = {Elsevier}, 8049 title = {n-Monotone exact functionals}, 8050 volume = {347}, 8051 year = {2008} 8052 } 8053 8054 @proceedings{MTNS-2000, 8055 booktitle = {Fourteenth International Symposium on Mathematical Theory of Networks and systems: MTNS 2000}, 8056 title = {Fourteenth International Symposium on Mathematical Theory of Networks and systems: MTNS 2000}, 8057 year = {2000} 8058 } 8059 8060 @techreport{Troffaes-idmfacts, 8061 author = {Matthias C. M. Troffaes}, 8062 title = {The imprecise Dirichlet model: facts and formulas} 8063 } 8064 8065 @techreport{Berger-1993, 8066 annote = {ook op papier}, 8067 author = {James Berger}, 8068 institution = {Purdue University, Department of Statistics}, 8069 number = {93-53C}, 8070 title = {An Overview of Robust Bayesian Analysis}, 8071 year = {1993} 8072 } 8073 8074 @inproceedings{DeCooman-Miranda-2011, 8075 address = {Innsbruck, Austria}, 8076 author = {Gert {De Cooman} and Enrique Miranda}, 8077 booktitle = {ISIPTA'11: Proceedings of the Seventh International Symposium on Imprecise Probability: Theories and Applications}, 8078 editor = {Frank Coolen and Gert {De Cooman} and Thomas Fetz and Michael Oberguggenberger}, 8079 pages = {169–178}, 8080 publisher = {SIPTA}, 8081 title = {Independent natural extension for sets of desirable gambles}, 8082 year = {2011} 8083 } 8084 8085 @article{Wagner-1997-old+new-III, 8086 annote = {op papier in Wagnerbundel}, 8087 author = {Carl G. Wagner}, 8088 journal = {Philosophy of Science}, 8089 pages = {165–175}, 8090 title = {Old Evidence and New Explanation}, 8091 volume = {68}, 8092 year = {2001} 8093 } 8094 8095 @misc{Fukuda-polyfaq, 8096 author = {Komei Fukuda}, 8097 title = {Frequently Asked Questions in Polyhedral Computation}, 8098 url = {http://www.ifor.math.ethz.ch/~fukuda/polyfaq/polyfaq.html}, 8099 year = {2004} 8100 } 8101 8102 @book{Jeffreys-1983, 8103 author = {Harold Jeffreys}, 8104 edition = {corrected}, 8105 publisher = {Oxford University Press}, 8106 title = {Theory of Probability}, 8107 year = {1983} 8108 } 8109 8110 @article{Daniell-1918, 8111 author = {P. J. Daniell}, 8112 journal = {The Annals of Mathematics}, 8113 localfile = {article/Daniell-1918.pdf}, 8114 number = {4}, 8115 pages = {279–294}, 8116 title = {A general form of integral}, 8117 url = {http://www.jstor.org/stable/1967495}, 8118 volume = {19}, 8119 year = {1918} 8120 } 8121 8122 @book{Hartfiel-1998-book, 8123 author = {Darald J. Hartfiel}, 8124 number = {1695}, 8125 publisher = {Springer}, 8126 series = {Lecture Notes in Mathematics}, 8127 title = {Markov Set-Chains}, 8128 url = {http://books.google.com/books?id=79wZAQAAIAAJ}, 8129 year = {1998} 8130 } 8131 8132 @book{Laplace-1920-theorie, 8133 author = {Pierre-Simon Laplace}, 8134 edition = {3}, 8135 publisher = {Gauthier-Villars}, 8136 series = {Oeuvres complètes de Laplace}, 8137 title = {Théorie analytique des probabilités}, 8138 volume = {7}, 8139 year = {1820} 8140 } 8141 8142 @incollection{DeCooman-Miranda-2007-symmetry, 8143 address = {London}, 8144 annote = {in svn-repo}, 8145 author = {Gert {De Cooman} and Enrique Miranda}, 8146 booktitle = {Probability and Inference: Essays in Honor of Henry E. Kyburg, Jr.}, 8147 editor = {William Harper and Gregory Wheeler}, 8148 pages = {67–149}, 8149 publisher = {King's College Publications}, 8150 title = {Symmetry of models versus models of symmetry}, 8151 year = {2007} 8152 } 8153 8154 @article{Seidenfeld-Schervish-Kadane-1995-preference, 8155 author = {Teddy Seidenfeld and Mark J. Schervish and Joseph B. Kadane}, 8156 doi = {10.1214/aos}, 8157 journal = {The Annals of Statistics}, 8158 keywords = {Axioms of decision theory; partial order; robust}, 8159 localfile = {article/Seidenfeld-Schervish-Kadane-1995-preference.pdf}, 8160 month = dec, 8161 number = {6}, 8162 pages = {2168–2217}, 8163 publisher = {Institute of Mathematical Statistics}, 8164 title = {A representation of partially ordered preferences}, 8165 volume = {23}, 8166 year = {1995} 8167 } 8168 8169 @article{Kaplan-etal-2011, 8170 abstract = {During early stages of development, regulatory proteins bind 8171 DNA and control the expression of nearby genes, thereby driving spatial and 8172 temporal patterns of gene expression during development. But the biochemical 8173 forces that determine where these regulatory proteins bind are poorly 8174 understood. We gathered experimental data on the activities of several key 8175 regulators of early development of the fruit fly (Drosophila melanogaster) and 8176 developed a computational method to predict where and how strongly they will 8177 bind. We find that competition, cooperativity, and other interactions among 8178 individual regulatory proteins have a limited effect on their binding, while the 8179 global accessibility of DNA to protein binding has a significant impact on the 8180 binding of all factors. Our results suggest a practical method for predicting 8181 regulatory binding by combining experimental DNA accessibility assays with 8182 computational algorithms to determine where will binding occur among the 8183 accessible regions of the genome.}, 8184 author = {Tommy Kaplan and Li Xiao-Yong and Peter J. Sabo and Sean Thomas and John A Stamatoyannopoulos and Mark D. Biggin and Michael B. Eisen}, 8185 doi = {10.1371/journal.pgen.1001290}, 8186 journal = {PLoS Genetics}, 8187 localfile = {article/Kaplan-etal-2011.pdf}, 8188 number = {2}, 8189 pages = {e1001290}, 8190 publisher = {Public Library of Science}, 8191 title = {Quantitative Models of the Mechanisms That Control Genome-Wide Patterns of Transcription Factor Binding during Early Drosophila Development}, 8192 volume = {7}, 8193 year = {2011} 8194 } 8195 8196 @article{Efron-1978-expfam, 8197 abstract = {There are two important spaces connected with every 8198 multivariate exponential family, the natural parameter space and the expectation 8199 parameter space. We describe some geometric results relating the two. (In the 8200 simplest case, that of a normal translation family, the two spaces coincide and 8201 the geometry is the familiar Euclidean one.) Maximum likelihood estimation, 8202 within one-parameter curved subfamilies of the multivariate family, has two 8203 simple and useful geometric interpretations. The geometry also relates to the 8204 Fisherian question: to what extent can the Fisher information be replaced by 8205 -\partial^2/\partial$\theta$^2\lbrack\log 8206 f\_$\theta$(x)\rbrack\mid\_{$\theta$=\hat{$\theta$}} in the variance bound for 8207 \hat{$\theta$}, the maximum likelihood estimator?}, 8208 author = {Bradley Efron}, 8209 doi = {10.1214/aos}, 8210 issn = {0090-5364}, 8211 journal = {The Annals of Statistics}, 8212 keywords = {Curvature; Kullback-Leibler distance; duality; maximum likelihood estimation}, 8213 localfile = {article/Efron-1978-expfam.pdf}, 8214 month = mar, 8215 number = {2}, 8216 pages = {362–376}, 8217 publisher = {Institute of Mathematical Statistics}, 8218 title = {The geometry of exponential families}, 8219 volume = {6}, 8220 year = {1978} 8221 } 8222 8223 @article{Consonni-Veronese-2001, 8224 abstract = {Consider a standard conjugate family of prior distributions 8225 for a vector-parameter indexing an exponential family. Two distinct model 8226 parameterizations may well lead to standard conjugate families which are not 8227 consistent, i.e. one family cannot be derived from the other by the usual 8228 change-of-variable technique. This raises the problem of finding suitable 8229 parameterizations that may lead to enriched conjugate families which are more 8230 flexible than the traditional ones. The previous remark motivates the definition 8231 of a new property for an exponential family, named conditional reducibility. 8232 Features of conditionally-reducible natural exponential families are 8233 investigated thoroughly. In particular, we relate this new property to the 8234 notion of cut, and show that conditionally-reducible families admit a 8235 reparameterization in terms of a vector having likelihood-independent 8236 components. A general methodology to obtain enriched conjugate distributions for 8237 conditionally-reducible families is described in detail, generalizing previous 8238 works and more recent contributions in the area. The theory is illustrated with 8239 reference to natural exponential families having simple quadratic variance 8240 function.}, 8241 author = {Guido Consonni and Piero Veronese}, 8242 doi = {10.1111/1467-9469.00243}, 8243 journal = {Scandinavian Journal of Statistics}, 8244 keywords = {Bayesian inference; conditional reducibility; cut; enriched prior; exponential family; simple quadratic variance function}, 8245 localfile = {article/Consonni-Veronese-2001.pdf}, 8246 number = {2}, 8247 pages = {377–406}, 8248 title = {Conditionally Reducible Natural Exponential Families and Enriched Conjugate Priors}, 8249 volume = {28}, 8250 year = {2001} 8251 } 8252 8253 @article{Lodwick-Bachman-2005, 8254 abstract = {Fuzzy and possibilistic optimization methods are 8255 demonstrated to be effective tools in solving large-scale problems. In 8256 particular, an optimization problem in radiation therapy with various orders of 8257 complexity from 1000 to 62,250 constraints for fuzzy and possibilistic linear 8258 and nonlinear programming implementations possessing (1) fuzzy or soft 8259 inequalities, (2) fuzzy right-hand side values, and (3) possibilistic right-hand 8260 side is used to demonstrate that fuzzy and possibilistic optimization methods 8261 are tractable and useful. We focus on the uncertainty in the right side of 8262 constraints which arises, in the context of the radiation therapy problem, from 8263 the fact that minimal and maximal radiation tolerances are ranges of values, 8264 with preferences within the range whose values are based on research results, 8265 empirical findings, and expert knowledge, rather than fixed real numbers. The 8266 results indicate that fuzzy/possibilistic optimization is a natural and 8267 effective way to model various types of optimization under uncertainty problems 8268 and that large fuzzy and possibilistic optimization problems can be solved 8269 efficiently.}, 8270 author = {Weldon A. Lodwick and Katherine Bachman}, 8271 doi = {10.1007/s10700-005-3663-4}, 8272 issn = {1568-4539}, 8273 journal = {Fuzzy Optimization and Decision Making}, 8274 localfile = {article/Lodwick-Bachman-2005.pdf}, 8275 pages = {257–278}, 8276 publisher = {Springer Netherlands}, 8277 title = {Solving Large-Scale Fuzzy and Possibilistic Optimization Problems}, 8278 volume = {4}, 8279 year = {2005} 8280 } 8281 8282 @article{Goldberg-1991-float, 8283 abstract = {Floating-point arithmetic is considered as esoteric subject 8284 by many people. This is rather surprising, because floating-point is ubiquitous 8285 in computer systems: Almost every language has a floating-point datatype; 8286 computers from PCs to supercomputers have floating-point accelerators; most 8287 compilers will be called upon to compile floating-point algorithms from time to 8288 time; and virtually every operating system must respond to floating-point 8289 exceptions such as overflow. This paper presents a tutorial on the aspects of 8290 floating-point that have a direct impact on designers of computer systems. It 8291 begins with background on floating-point representation and rounding error, 8292 continues with a discussion of the IEEE floating point standard, and concludes 8293 with examples of how computer system builders can better support floating 8294 point.}, 8295 author = {David Goldberg}, 8296 doi = {10.1145/103162.103163}, 8297 issn = {0360-0300}, 8298 journal = {ACM Computing Surveys}, 8299 localfile = {article/Goldberg-1991-float.pdf}, 8300 month = mar, 8301 number = {1}, 8302 pages = {5–48}, 8303 publisher = {ACM}, 8304 title = {What every computer scientist should know about floating-point arithmetic}, 8305 url = {http://portal.acm.org/citation.cfm?doid=103162.103163}, 8306 volume = {23}, 8307 year = {1991} 8308 } 8309 8310 @article{Davis-1954, 8311 author = {Chandler Davis}, 8312 issn = {0002-9327}, 8313 journal = {American Journal of Mathematics}, 8314 localfile = {article/Davis-1954.pdf}, 8315 number = {4}, 8316 pages = {733–746}, 8317 publisher = {The Johns Hopkins University Press}, 8318 title = {Theory of positive linear dependence}, 8319 url = {http://www.jstor.org/stable/2372648}, 8320 volume = {76}, 8321 year = {1954} 8322 } 8323 8324 @techreport{Hutter-2006, 8325 address = {Manno-Lugano, Switzerland}, 8326 author = {Marcus Hutter}, 8327 institution = {IDSIA}, 8328 number = {IDSIA-03-06}, 8329 title = {On the Foundations of Universal Sequence Prediction}, 8330 year = {2006} 8331 } 8332 8333 @article{Wagner-2002-probkin+comm, 8334 annote = {op papier in Wagnerbundel}, 8335 author = {Carl G. Wagner}, 8336 journal = {Philosophy of Science}, 8337 pages = {266–278}, 8338 title = {Probability Kinematics and Commutativity}, 8339 volume = {69}, 8340 year = {2002} 8341 } 8342 8343 @proceedings{FMMES-1974, 8344 address = {Warsaw}, 8345 booktitle = {Formal methods in the methodology of empirical sciences}, 8346 editor = {Marian Przełęcki and Klemens Szaniawski}, 8347 publisher = {D. Reidel Publishing Company, Dordrecht, Holland / Boston, U.S.A; Ossolineum Publishing company, Wrocław, Poland}, 8348 title = {Proceedings of the conference for formal methods in the methodology of empirical sciences}, 8349 year = {1974} 8350 } 8351 8352 @article{Grabisch-1995, 8353 author = {Michel Grabisch}, 8354 journal = {IEEE Transactions on Fuzzy Systems}, 8355 localfile = {article/Grabisch-1995.pdf}, 8356 number = {1}, 8357 pages = {96–109}, 8358 title = {On Equivalence Classes of Fuzzy Connectives—The Case of Fuzzy Integrals}, 8359 volume = {3}, 8360 year = {1995} 8361 } 8362 8363 @article{Hartfiel-Seneta-1994, 8364 abstract = {In the theory of homogeneous Markov chains, states are 8365 classified according to their connectivity to other states and this 8366 classification leads to a classification of the Markov chains themselves. In 8367 this paper we classify Markov set-chains analogously, particularly into ergodic, 8368 regular, and absorbing Markov set-chains. A weak law of large numbers is 8369 developed for regular Markov set-chains. Examples are used to illustrate 8370 analysis of behavior of Markov set-chains.}, 8371 author = {Darald J. Hartfiel and E. Seneta}, 8372 issn = {0001-8678}, 8373 journal = {Advances in Applied Probability}, 8374 localfile = {article/Hartfiel-Seneta-1994.pdf}, 8375 number = {4}, 8376 pages = {947–964}, 8377 publisher = {Applied Probability Trust}, 8378 title = {On the theory of Markov set-chains}, 8379 url = {http://www.jstor.org/stable/1427899}, 8380 volume = {26}, 8381 year = {1994} 8382 } 8383 8384 @techreport{Griffiths-Ghahramani-2005, 8385 author = {Thomas L. Griffiths and Zoubin Ghahramani}, 8386 institution = {Gatsby Unit, University College London}, 8387 number = {GCNU TR 2005-001}, 8388 title = {Infinite Latent Feature Models and the Indian Buffet Process}, 8389 year = {2005} 8390 } 8391 8392 @article{Destercke-etal-2008-unifying1, 8393 author = {Sébastien Destercke and Didier Dubois and E. Chojnacki}, 8394 doi = {10.1016/j.ijar.2008.07.003}, 8395 journal = {International Journal of Approximate Reasoning}, 8396 localfile = {article/Destercke-etal-2008-unifying1.pdf}, 8397 pages = {649–663}, 8398 title = {Unifying practical uncertainty representations: I. Generalized p-boxes}, 8399 volume = {49}, 8400 year = {2008} 8401 } 8402 8403 @incollection{Henk-RichterGebert-Ziegler-1997, 8404 author = {Martin Henk and Jürgen Richter-Gebert and Günter M. Ziegler}, 8405 booktitle = {Handbook of Discrete and Computational Geometry}, 8406 editor = {J. E. Goodman and J. O'Rourke}, 8407 pages = {243–270}, 8408 publisher = {CRC Press}, 8409 title = {Basic properties of convex polytopes}, 8410 url = {http://fma2.math.uni-magdeburg.de/~henk/preprints/henk; richter-gebert ziegler&basic properties of convex polytopes.pdf}, 8411 year = {1997} 8412 } 8413 8414 @article{Levi-1974, 8415 author = {Isaac Levi}, 8416 journal = {The Journal of Philosophy}, 8417 localfile = {article/Levi-1974.pdf}, 8418 number = {13}, 8419 pages = {391–418}, 8420 title = {On indeterminate probabilities}, 8421 url = {http://www.jstor.org/stable/2025161}, 8422 volume = {71}, 8423 year = {1974} 8424 } 8425 8426 @article{Huang-Huang-Tsai-2006-Hilbert-metric, 8427 abstract = {The purpose of this paper is to study the eigenvalue 8428 problems for a class of positive nonlinear operators. Using projective metric 8429 techniques and the contraction mapping principle, we establish existence, 8430 uniqueness and continuity results for positive eigensolutions of a particular 8431 type of positive nonlinear operator. In addition, we prove the existence of a 8432 unique fixed point of the operator with explicit norm-estimates. Applications to 8433 nonlinear systems of equations and to matrix equations are considered.}, 8434 author = {Min-Jei Huang and Chao-Ya Huang and Tzong-Mo Tsai}, 8435 doi = {10.1016/j.laa.2005.08.024}, 8436 journal = {Linear Algebra and its Applications}, 8437 keywords = {Concave operator; Cone; Eigenvalue problem; Hilbert’s projective metric; Matrix equation; Nonlinear system of equations}, 8438 localfile = {article/Huang-Huang-Tsai-2006-Hilbert-metric.pdf}, 8439 number = {1}, 8440 pages = {202–211}, 8441 title = {Applications of Hilbert's projective metric to a class of positive nonlinear operators}, 8442 volume = {413}, 8443 year = {2006} 8444 } 8445 8446 @book{Koller-Friedman-2009, 8447 author = {Daphne Koller and Nir Friedman}, 8448 isbn = {978-0-262-01319-2}, 8449 publisher = {MIT Press}, 8450 series = {Adaptive Computation and Machine Learning}, 8451 title = {Probabilistic Graphical Models}, 8452 year = {2009} 8453 } 8454 8455 @mastersthesis{Dhaenens-2007, 8456 author = {Stefaan Dhaenens}, 8457 localfile = {mastersthesis/Dhaenens-2007.pdf}, 8458 school = {Universiteit Gent}, 8459 title = {Onderzoek van Imprecieze Markov-modellen}, 8460 url = {http://hdl.handle.net/1854/LU-470245}, 8461 year = {2007} 8462 } 8463 8464 @article{Nau-2006-shape, 8465 abstract = {Incomplete preferences provide the epistemic foundation for 8466 models of imprecise subjective probabilities and utilities that are used in 8467 robust Bayesian analysis and in theories of bounded rationality. This paper 8468 presents a simple axiomatization of incomplete preferences and characterizes the 8469 shape of their representing sets of probabilities and utilities. Deletion of the 8470 completeness assumption from the axiom system of Anscombe and Aumann yields 8471 preferences represented by a convex set of state-dependent expected utilities, 8472 of which at least one must be a probability/utility pair. A strengthening of the 8473 state-independence axiom is needed to obtain a representation purely in terms of 8474 a set of probability/utility pairs.}, 8475 author = {Robert F. Nau}, 8476 doi = {10.1214/009053606000000740}, 8477 journal = {The Annals of Statistics}, 8478 keywords = {Axioms of decision theory; Bayesian robustness; coherence; imprecise probabilities and utilities; partial order; state-dependent utility}, 8479 localfile = {article/Nau-2006-shape.pdf}, 8480 number = {5}, 8481 pages = {2430–2448}, 8482 title = {The shape of incomplete preferences}, 8483 volume = {34}, 8484 year = {2006} 8485 } 8486 8487 @misc{Doumont-2001-internet, 8488 author = {Jean-luc Doumont}, 8489 title = {How Internet works}, 8490 year = {2001} 8491 } 8492 8493 @article{Miranda-DeCooman-Quaeghebeur-2007-finitely, 8494 abstract = {We study the information that a distribution function 8495 provides about the finitely additive probability measure inducing it. We show 8496 that in general there is an infinite number of finitely additive probabilities 8497 associated with the same distribution function. Secondly, we investigate the 8498 relationship between a distribution function and its given sequence of moments. 8499 We provide formulae for the sets of distribution functions, and finitely 8500 additive probabilities, associated with some moment sequence, and determine 8501 under which conditions the moments determine the distribution function uniquely. 8502 We show that all these problems can be addressed efficiently using the theory of 8503 coherent lower previsions.}, 8504 author = {Enrique Miranda and Gert {De Cooman} and Erik Quaeghebeur}, 8505 doi = {10.1016/j.ijar.2007.07.007}, 8506 journal = {International Journal of Approximate Reasoning}, 8507 localfile = {article/Miranda-DeCooman-Quaeghebeur-2007-finitely.pdf}, 8508 number = {1}, 8509 pages = {132–155}, 8510 title = {Finitely additive extensions of distribution functions and moment sequences: The coherent lower prevision approach}, 8511 volume = {48}, 8512 year = {2008} 8513 } 8514 8515 @inproceedings{Fukuda-Prodon-1996-cdd, 8516 author = {Komei Fukuda and Alain Prodon}, 8517 booktitle = {Combinatorics and Computer Science}, 8518 doi = {10.1007/3-540-61576-8_77}, 8519 editor = {M. Deza and R. Euler and I. Manoussakis}, 8520 pages = {91–111}, 8521 publisher = {Springer-Verlag}, 8522 series = {Lecture Notes in Computer Science}, 8523 title = {Double Description Method Revisited}, 8524 url = {http://www.ifor.math.ethz.ch/~fukuda/cdd_home}, 8525 volume = {1120}, 8526 year = {1996} 8527 } 8528 8529 @book{Pearl-1988, 8530 address = {San Francisco, California}, 8531 author = {Judea Pearl}, 8532 publisher = {Morgan Kaufmann}, 8533 title = {Probabilistic Reasoning in Intelligent Systems}, 8534 year = {1988} 8535 } 8536 8537 @article{Mraz-1998, 8538 abstract = {The paper deals with computing the exact upper and lower 8539 bounds of optimal values forlinear programming problems whose coefficients vary 8540 in given intervals. The theoreticalbackground for calculating these bounds is 8541 described and corresponding algorithms aregiven. A comparison with other 8542 approaches, some applications and a software package arementioned.}, 8543 author = {František Mráz}, 8544 doi = {10.1023/A:1018985914065}, 8545 issn = {0254-5330}, 8546 journal = {Annals of Operations Research}, 8547 keywords = {inexact data; interval coefficients; linear programming problem}, 8548 localfile = {article/Mraz-1998.pdf}, 8549 pages = {51–62}, 8550 publisher = {Springer}, 8551 title = {Calculating the exact bounds of optimal valuesin LP with interval coefficients}, 8552 volume = {81}, 8553 year = {1998} 8554 } 8555 8556 @article{Aach-Church-2001, 8557 annote = {ook op papier}, 8558 author = {John Aach and George M. Church}, 8559 doi = {10.1093/bioinformatics}, 8560 journal = {Bioinformatics}, 8561 localfile = {article/Aach-Church-2001.pdf}, 8562 pages = {495–508}, 8563 title = {Aligning gene expression time series with time warping algorithms}, 8564 volume = {17}, 8565 year = {2001} 8566 } 8567 8568 @article{DeFinetti-1967, 8569 author = {Bruno de Finetti}, 8570 journal = {Revue Roumaine des Mathémathiques Pures et Appliquées}, 8571 pages = {1227–1233}, 8572 title = {Quelques conventions qui semblent utiles}, 8573 volume = {12}, 8574 year = {1967} 8575 } 8576 8577 @techreport{Kaymak-Sousa-2001, 8578 abstract = {Many practical optimization problems are characterized by 8579 some flexibility in the problem constraints, where this flexibility can be 8580 exploited for additional trade-off between improving the objective function and 8581 satisfying the constraints. Especially in decision making, this type of 8582 flexibility could lead to workable solutions, where the goals and the 8583 constraints specified by different parties involved in the decision making are 8584 traded off against one another and satisfied to various degrees. Fuzzy sets have 8585 proven to be a suitable representation for modeling this type of soft 8586 constraints. Conventionally, the fuzzy optimization problem in such a setting is 8587 defined as the simultaneous satisfaction of the constraints and the goals. No 8588 additional distinction is assumed to exist amongst the constraints and the 8589 goals. This report proposes an extension of this model for satisfying the 8590 problem constraints and the goals, where preference for different constraints 8591 and goals can be specified by the decision-maker. The difference in the 8592 preference for the constraints is represented by a set of associated weight 8593 factors, which influence the nature of trade-off between improving the 8594 optimization objectives and satisfying various constraints. Simultaneous 8595 weighted satisfaction of various criteria is modeled by using the recently 8596 proposed weighted extensions of Archimedean) fuzzy t-norms. The weighted 8597 satisfaction of the problem constraints and goals are demonstrated by using a 8598 simple general, and it can also be applied to fuzzy mathematical programming 8599 problems and multi-objective fuzzy optimization.}, 8600 author = {U. Kaymak and J. M. Sousa}, 8601 institution = {Erasmus Universiteit Amsterdam}, 8602 number = {ERS-2001-19-LIS}, 8603 title = {Weighted constraints in fuzzy optimization}, 8604 url = {http://repub.eur.nl/res/pub/85}, 8605 year = {2001} 8606 } 8607 8608 @book{Dunford-Schwartz-1958, 8609 address = {New York}, 8610 author = {Nelson Dunford and Jacob T. Schwartz}, 8611 publisher = {Interscience Publishers}, 8612 series = {Pure and Applied Mathematics}, 8613 title = {Linear Operators Part I}, 8614 volume = {VII}, 8615 year = {1958} 8616 } 8617 8618 @article{DeCooman-Troffaes-2004, 8619 abstract = {We discuss why coherent lower previsions provide a good 8620 uncertainty model for solving generic uncertainty problems involving possibly 8621 conflicting expert information. We study various ways of combining expert 8622 assessments on different domains, such as natural extension, independent natural 8623 extension and the type-I product, as well as on common domains, such as 8624 conjunction and disjunction. We provide each of these with a clear 8625 interpretation, and we study how they are related. Observing that in combining 8626 expert assessments no information is available about the order in which they 8627 should be combined, we suggest that the final result should be independent of 8628 the order of combination. The rules of combination we study here satisfy this 8629 requirement.}, 8630 annote = {reprint}, 8631 author = {Gert {De Cooman} and Matthias C. M. Troffaes}, 8632 doi = {10.1016/j.ress.2004.03.007}, 8633 journal = {Reliability Engineering \& System Safety}, 8634 keywords = {coherent lower previsions; conjunction; disjunction; expert information; independence; marginal extension; natural extension; type-1 product}, 8635 localfile = {article/DeCooman-Troffaes-2004.pdf}, 8636 number = {1}, 8637 pages = {113–134}, 8638 publisher = {Elsevier}, 8639 title = {Coherent lower previsions in systems modelling: products and aggregation rules}, 8640 volume = {85}, 8641 year = {2004} 8642 } 8643 8644 @book{Menezes-VanOorschot-Vanstone-1996, 8645 author = {Alfred J. Menezes and Paul C. {Van Oorschot} and Scott A. Vanstone}, 8646 publisher = {CRC Press}, 8647 title = {Handbook of Applied Cryptography}, 8648 year = {1996} 8649 } 8650 8651 @article{Choquet-1954, 8652 abstract = {C'est un essai de théorie générale des fonctions croissantes 8653 d'ensemble. On est amené à mettre en évidence diverses classes importantes de 8654 telles fonctions, en particulier la classe des fonctions fortement 8655 sous-additives, pour lesquelles existe une théorie analogue à celle de la 8656 mesure, et une sous-classe de celle-ci, à savoir la classe des fonctions 8657 alternées d'ordre infini, analogues aux fonctions numériques complètement 8658 monotones. La capacité classique est une telle fonction d'ensemble ; il en 8659 résulte l'identité des capacités intérieure et extérieure de tout ensemble 8660 borélien ou analytique. Un outil de recherche puissant est la représentation 8661 intégrale des fonctions d'une classe additive et convexe au moyen des éléments 8662 extrémaux d'une telle classe. Cette représentation permet d'identifier les 8663 fonctions alternées d'ordre infini avec certaines probabilités associées à 8664 l'ensemble variable.}, 8665 author = {Gustave Choquet}, 8666 doi = {10.5802/aif.53}, 8667 journal = {Annales de l'Institut Fourier}, 8668 localfile = {article/Choquet-1954.pdf}, 8669 pages = {131–295}, 8670 title = {Theory of capacities}, 8671 url = {http://www.numdam.org/item?id=AIF_1954__5__131_0}, 8672 volume = {5}, 8673 year = {1954} 8674 } 8675 8676 @inproceedings{Miranda-DeCooman-Quaeghebeur-2006-IPMU, 8677 address = {Paris}, 8678 author = {Enrique Miranda and Gert {De Cooman} and Erik Quaeghebeur}, 8679 booktitle = {Proceedings of the Eleventh International Conference on Information Processing and Management of Uncertainty in Knowledge-based Systems}, 8680 pages = {89–96}, 8681 title = {The moment problem for finitely additive probabilities}, 8682 volume = {1}, 8683 year = {2006} 8684 } 8685 8686 @article{Wagner-1997-old+new-II, 8687 annote = {op papier in Wagnerbundel}, 8688 author = {Carl G. Wagner}, 8689 journal = {Philosophy of Science}, 8690 pages = {283–288}, 8691 title = {Old Evidence and New Explanation}, 8692 volume = {66}, 8693 year = {1999} 8694 } 8695 8696 @article{Hartman-Watson-1974, 8697 author = {Philip Hartman and Geoffrey S. Watson}, 8698 doi = {10.1214/aop}, 8699 journal = {The Annals of Probability}, 8700 localfile = {article/Hartman-Watson-1974.pdf}, 8701 month = aug, 8702 number = {4}, 8703 pages = {593–607}, 8704 title = {“Normal” distribution functions on spheres and the modified Bessel functions}, 8705 volume = {2}, 8706 year = {1974} 8707 } 8708 8709 @article{Grunbaum-Shepard-1969, 8710 author = {Branko Grünbaum and G. C. Shepard}, 8711 doi = {10.1112/blms}, 8712 journal = {Bulletin of the London Mathematical Society}, 8713 localfile = {article/Grunbaum-Shepard-1969.pdf}, 8714 pages = {257–300}, 8715 publisher = {Springer Verlag}, 8716 title = {Convex polytopes}, 8717 volume = {1}, 8718 year = {1969} 8719 } 8720 8721 @misc{Quaeghebeur-murasyp, 8722 author = {Erik Quaeghebeur}, 8723 title = {murasyp: Python software for accept/reject statement-based uncertainty modeling}, 8724 url = {http://equaeghe.github.com/murasyp}, 8725 year = {in progress} 8726 } 8727 8728 @inproceedings{Schrage-IJzendoorn-VanderGaag-2005, 8729 author = {Martijn M. Schrage and Arjan van IJzendoorn and Linda C. van der Gaag}, 8730 booktitle = {Haskell '05: Proceedings of the 2005 ACM SIGPLAN Workshop on Haskell}, 8731 doi = {10.1145/1088348.1088351}, 8732 isbn = {1-59593-071-X}, 8733 location = {Tallinn, Estonia}, 8734 month = sep, 8735 pages = {17–26}, 8736 publisher = {ACM Press}, 8737 title = {Haskell ready to Dazzle the real world}, 8738 url = {http://www.cs.uu.nl/dazzle}, 8739 year = {2005} 8740 } 8741 8742 @article{Quaeghebeur-DeCooman-Hermans-2012, 8743 author = {Erik Quaeghebeur and Gert {De Cooman} and Filip Hermans}, 8744 note = {Journal paper}, 8745 title = {Accept \& Reject Statement-Based Uncertainty Models}, 8746 year = {in preparation} 8747 } 8748 8749 @inproceedings{VanderGaag-etal-2010-BNAIC, 8750 author = {Linda C. van der Gaag and Silja Renooij and Hermi J. M. Schijf and A. R. Elbers and W. L. Loeffen}, 8751 booktitle = {BNAIC 2010: Proceedings of the 22nd Benelux Conference on Artificial Intelligence}, 8752 location = {Luxembourg}, 8753 title = {Probability assessments from multiple experts: qualitative information is more robust}, 8754 year = {2010} 8755 } 8756 8757 @article{Coupe-VanderGaag-2002, 8758 abstract = {The assessments for the various conditional probabilities of 8759 a Bayesian belief network inevitably are inaccurate, influencing the reliability 8760 of its output. By subjecting the network to a sensitivity analysis with respect 8761 to its conditional probabilities, the reliability of its output can be 8762 investigated. Unfortunately, straightforward sensitivity analysis of a belief 8763 network is highly time-consuming. In this paper, we show that by qualitative 8764 considerations several analyses can be identified as being uninformative as the 8765 conditional probabilities under study cannot affect the output. In addition, we 8766 show that the analyses that are informative comply with simple mathematical 8767 functions. More specifically, we show that a belief network's output can be 8768 expressed as a quotient of two functions that are linear in a conditional 8769 probability under study. These properties allow for considerably reducing the 8770 computational burden of sensitivity analysis of Bayesian belief networks.}, 8771 author = {Veerle M. H. Coupé and Linda C. van der Gaag}, 8772 doi = {10.1023/A:1016398407857}, 8773 issn = {1012-2443}, 8774 journal = {Annals of Mathematics and Artificial Intelligence}, 8775 number = {4}, 8776 pages = {323–356}, 8777 publisher = {Springer Netherlands}, 8778 title = {Properties of sensitivity analysis of Bayesian belief networks}, 8779 volume = {36}, 8780 year = {2002} 8781 } 8782 8783 @inproceedings{VanderGaag-Renooij-2004, 8784 author = {Linda C. van der Gaag and Silja Renooij}, 8785 booktitle = {IPMU : Proceedings of the Tenth International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems}, 8786 location = {Perugia}, 8787 pages = {1675–1682}, 8788 title = {On the sensitivity of probabilistic networks to test reliability}, 8789 year = {2004} 8790 } 8791 8792 @inproceedings{Renooij-VanderGaag-2004-UAI, 8793 author = {Silja Renooij and Linda C. van der Gaag}, 8794 booktitle = {UAI-04: Proceedings of the Twentieth Conference on Uncertainty in Artificial Intelligence}, 8795 isbn = {0-9749039-0-6}, 8796 location = {Banff, Canada}, 8797 pages = {479–486}, 8798 publisher = {AUAI Press}, 8799 title = {Evidence-invariant sensitivity bounds}, 8800 year = {2004} 8801 } 8802 8803 @inproceedings{Kjaerulff-VanderGaag-2000, 8804 author = {Uffe Kjærulff and Linda C. van der Gaag}, 8805 booktitle = {UAI-00: Proceedings of the Sixteenth Conference on Uncertainty in Artificial Intelligence}, 8806 editor = {Craig Boutilier and Moisés Goldszmidt}, 8807 isbn = {1-55860-709-9}, 8808 pages = {317–325}, 8809 publisher = {Morgan Kaufmann}, 8810 title = {Making Sensitivity Analysis Computationally Efficient.}, 8811 year = {2000} 8812 } 8813 8814 @inproceedings{VanderGaag-Renooij-2001, 8815 author = {Linda C. van der Gaag and Silja Renooij}, 8816 booktitle = {UAI-01: Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence}, 8817 editor = {Jack S. Breese and Daphne Koller}, 8818 isbn = {1-55860-800-1}, 8819 pages = {530–537}, 8820 publisher = {Morgan Kaufmann}, 8821 title = {Analysing sensitivity data from probabilistic networks}, 8822 year = 2001 8823 } 8824 8825 @incollection{deFinetti-1937-foresight, 8826 author = {Bruno de Finetti}, 8827 booktitle = {Studies in Subjective Probability}, 8828 editor = {Henry E Kyburg and Smokler}, 8829 localfile = {inbook/deFinetti-1937-foresight.pdf}, 8830 pages = {93–158}, 8831 publisher = {Wiley}, 8832 title = {Foresight: Its Logical Laws, Its Subjective Sources}, 8833 year = {1964} 8834 } 8835 8836 @article{DeCampos-etal-2009, 8837 abstract = {This paper explores the application of semi-qualitative 8838 probabilistic networks (SQPNs) that combine numeric and qualitative information 8839 to computer vision problems. Our version of SQPN allows qualitative influences 8840 and imprecise probability measures using intervals. We describe an Imprecise 8841 Dirichlet model for parameter learning and an iterative algorithm for evaluating 8842 posterior probabilities, maximum a posteriori and most probable explanations. 8843 Experiments on facial expression recognition and image segmentation problems are 8844 performed using real data.}, 8845 annote = {doi: 10.1080/15598608.2009.10411920}, 8846 author = {Cassio Polpo de Campos and Lei Zhang and Yan Tong and Qiang Ji}, 8847 doi = {10.1080/15598608.2009.10411920}, 8848 issn = {1559-8608}, 8849 journal = {Journal of Statistical Theory and Practice}, 8850 keywords = {Computer vision applications; Imprecise probabilities; Probabilistic networks; Qualitative relations}, 8851 localfile = {article/DeCampos-etal-2009.pdf}, 8852 month = mar, 8853 number = {1}, 8854 pages = {197–210}, 8855 publisher = {Taylor \& Francis}, 8856 title = {Semi-Qualitative Probabilistic Networks in Computer Vision Problems}, 8857 volume = {3}, 8858 year = {2009} 8859 } 8860 8861 @article{DeFinetti-Jacob-1935, 8862 author = {Bruno de Finetti and M. Jacob}, 8863 journal = {Giornale dell'Istituto italiano degli attuari}, 8864 localfile = {article/DeFinetti-Jacob-1935.pdf}, 8865 pages = {303–319}, 8866 title = {Sull'integrale di Stieltjes-Riemann}, 8867 volume = {6}, 8868 year = {1935} 8869 } 8870 8871 @article{Hampel2009, 8872 abstract = {The paper gives a short survey about the occurrence 8873 (sometimes hidden in the background) of nonadditive probabilities in statistics. 8874 It starts with the original meaning of ?probability? in statistics in the Ars 8875 Conjectandi by Jakob (James) Bernoulli, and the ensuing misunderstanding which 8876 gave the term its present meaning. One chapter is about robustness theory, its 8877 use of (nonadditive) Choquet-capacities, and an attempt to clarify some 8878 widespread misunderstandings about it, which have consequences for the use of 8879 upper and lower probabilities. Also the uncertainty about model choice 8880 (including the conflict between purely mathematical reasoning and good 8881 statistical practice) and treatment of outliers is briefly discussed. The 8882 partial arbitrariness of additivity both in Bayes' famous Scholium and in modern 8883 Bayes theory is outlined. The infamous and almost forgotten fiducial 8884 probabilities can actually be corrected and find their place in a more general 8885 paradigm using upper and lower probabilities. Finally, a new (?) qualitative 8886 theory of inference is mentioned which may contain some essentials of inductive 8887 reasoning in real life.}, 8888 author = {Frank Hampel}, 8889 doi = {10.1080/15598608.2009.10411908}, 8890 issn = {1559-8608}, 8891 journal = {Journal of Statistical Theory and Practice}, 8892 keywords = {Ars Conjectandi; Bayes’ Scholium; Inaccuracy and uncertainty; Misleading logic in data analysis; Misunder- standings about robustness theory; Nonadditive probabilites; Original meaning of probability; Proper fiducial probabilities; Qualitative reasoning in real life.}, 8893 localfile = {article/Hampel-2009.pdf}, 8894 month = mar, 8895 number = {1}, 8896 pages = {11–23}, 8897 publisher = {Taylor \& Francis}, 8898 title = {Nonadditive Probabilities in Statistics}, 8899 volume = {3}, 8900 year = {2009} 8901 } 8902 8903 @article{Kozine-Krymsky-2009, 8904 abstract = {This paper describes how one can compute interval-valued 8905 statistical measures given limited information about the underlying 8906 distribution. The particular focus is on a bounded derivative of a probability 8907 density function and its combination with other available statistical evidence 8908 for computing quantities of interest. To be able to utilise the evidence about 8909 the derivative it is suggested to adapt the ?conventional? problem statement to 8910 variational calculus and the way to do so is demonstrated. A number of examples 8911 are given throughout the paper.}, 8912 author = {Igor O. Kozine and Victor Krymsky}, 8913 doi = {10.1080/15598608.2009.10411909}, 8914 issn = {1559-8608}, 8915 journal = {Journal of Statistical Theory and Practice}, 8916 keywords = {Bounded derivative; Bounded probability distribution; Interval- valued measures; Natural extension; Variational calculus}, 8917 localfile = {article/Kozine-Krymsky-2009.pdf}, 8918 month = mar, 8919 number = {1}, 8920 pages = {25–38}, 8921 publisher = {Taylor \& Francis}, 8922 title = {Bounded Densities and Their Derivatives: Extension to other Domains}, 8923 volume = {3}, 8924 year = {2009} 8925 } 8926 8927 @article{Stoye-2009, 8928 abstract = {This paper applies recently developed methods to robust 8929 assessment of treatment outcomes and robust treatment choice based on 8930 nonexperimental data. The substantive question is whether young offenders should 8931 be assigned to residential or nonresidential treatment in order to prevent 8932 subsequent recidivism. A large data set on past offenders exists, but treatment 8933 assignment was by judges and not by experimenters, hence counterfactual outcomes 8934 are not identified unless one imposes strong assumptions. The analysis is 8935 carried out in two steps. First, I show how to compute identified bounds on 8936 expected outcomes under various assumptions that are too weak to restore 8937 conventional identification but may be accordingly credible. The bounds are 8938 estimated, and confidence regions that take current theoretical developments 8939 into account are computed. I then ask which treatment to assign to future 8940 offenders if the identity of the best treatment will not be learned from the 8941 data. This is a decision problem under ambiguity. I characterize and compute 8942 decision rules that are asymptotically efficient under the minimax regret 8943 criterion. The substantive conclusion is that both bounds and recommended 8944 decisions vary significantly across the assumptions. The data alone do not 8945 permit conclusions or decisions that are globally robust in the sense of holding 8946 uniformly over reasonable assumptions.}, 8947 author = {Jörg Stoye}, 8948 doi = {10.1080/15598608.2009.10411923}, 8949 issn = {1559-8608}, 8950 journal = {Journal of Statistical Theory and Practice}, 8951 keywords = {Bounds; Minimax regret; Partial identification; Statistical decision rules; Treatment choice; Treatment evaluation}, 8952 localfile = {article/Stoye-2009.pdf}, 8953 month = mar, 8954 number = {1}, 8955 pages = {239–254}, 8956 publisher = {Taylor \& Francis}, 8957 title = {Partial Identification and Robust Treatment Choice: An Application to Young Offenders}, 8958 volume = {3}, 8959 year = {2009} 8960 } 8961 8962 @article{CoolenSchrijner-etal-2009, 8963 abstract = {More and more often the traditional (classical) concept of 8964 probability, and the statistical methods based on it, have been criticized for 8965 being unable to cope with the multidimensional nature of uncertainty. Careful 8966 handling of imprecision is essential to draw reliable conclusions from complex 8967 data. This paper presents a short introductory discussion on the general area of 8968 imprecision in statistical theory and practice, and briefly introduces the 8969 further papers in this collection, demonstrating the importance of the adequate 8970 modelling of imprecision in different areas of application.}, 8971 author = {Pauline Coolen-Schrijner and Frank P. A. Coolen and Matthias C. M. Troffaes and Thomas Augustin}, 8972 doi = {10.1080/15598608.2009.10411907}, 8973 issn = {1559-8608}, 8974 journal = {Journal of Statistical Theory and Practice}, 8975 keywords = {Decision making; Elicition; Inference; Lower and upper probabilities; Robustness; Theory}, 8976 localfile = {article/CoolenSchrijner-etal-2009.pdf}, 8977 month = mar, 8978 number = {1}, 8979 pages = {1–9}, 8980 publisher = {Taylor \& Francis}, 8981 title = {Imprecision in Statistical Theory and Practice}, 8982 volume = {3}, 8983 year = {2009} 8984 } 8985 8986 @article{Pelessoni-Vicig-2009, 8987 abstract = {In this paper we consider some bounds for lower previsions 8988 that are either coherent or, more generally, centered convex. We focus on bounds 8989 concerning the classical product and Bayes' rules, discussing first weak product 8990 rules and some of their implications for coherent lower previsions. We then 8991 generalise a well-known lower bound, which is a (weak) version for events and 8992 coherent lower probabilities of Bayes' theorem, to the case of random variables 8993 and (centered) convex previsions. We obtain a family of bounds and show that one 8994 of them is undominated in all cases. Some applications are outlined, and it is 8995 shown that 2-monotonicity, which ensures that the bound is sharp in the case of 8996 events, plays a much more limited role in this general framework.}, 8997 author = {Renato Pelessoni and Paolo Vicig}, 8998 doi = {10.1080/15598608.2009.10411913}, 8999 issn = {1559-8608}, 9000 journal = {Journal of Statistical Theory and Practice}, 9001 keywords = {2-monotonicity; Bayes’ theorem; Centered convex previsions; Conditional lower previsions; Product rule}, 9002 localfile = {article/Pelessoni-Vicig-2009.pdf}, 9003 month = mar, 9004 number = {1}, 9005 pages = {85–101}, 9006 publisher = {Taylor \& Francis}, 9007 title = {Bayes' Theorem Bounds for Convex Lower Previsions}, 9008 volume = {3}, 9009 year = {2009} 9010 } 9011 9012 @article{Bose-2009-imposition, 9013 abstract = {We consider the problem of imposing shape constraints on a 9014 neighborhood class – the density ratio class (DeRobertis and Hartigan, 1981). 9015 Bose (1994) used mixture distributions to impose shape and smoothness 9016 constraints simultaneously. We discuss how one may impose either or both 9017 unimodality and symmetry without requiring simultaneous imposition of a 9018 smoothness constraint.}, 9019 author = {Sudip Bose}, 9020 doi = {10.1080/15598608.2009.10411910}, 9021 issn = {1559-8608}, 9022 journal = {Journal of Statistical Theory and Practice}, 9023 keywords = {Bayesian robustness; Convexity; Density bounded; Density ratio; Likelihood; Minimax; Neighborhood class; Posterior regret; Smoothness; Symmetry; Unimodality; $\Gamma$-minimax}, 9024 localfile = {article/Bose-2009-imposition.pdf}, 9025 month = mar, 9026 number = {1}, 9027 pages = {39–55}, 9028 publisher = {Taylor \& Francis}, 9029 title = {On the imposition of shape constraints in a robust Bayesian analysis}, 9030 volume = {3}, 9031 year = {2009} 9032 } 9033 9034 @article{Wilson-Huzurbazar-Sentz-2009, 9035 abstract = {In this paper we expand on recent advances in Bayesian 9036 inference for multilevel data in fault trees and Bayesian networks. As a first 9037 example, we compare the Bayesian fault tree and incomplete data approaches to 9038 statistical inference for multilevel data in fault trees. As a second example, 9039 we consider two a priori representations of uncertainty about the parameters of 9040 a Bayesian network: A multinomial-Dirichlet model and an extension of the 9041 imprecise Dirichlet model. We calculate the a posteriori uncertainty after 9042 updating with data using Markov chain Monte Carlo and compare the results.}, 9043 author = {Alyson G. Wilson and Aparna V. Huzurbazar and Kari Sentz}, 9044 doi = {10.1080/15598608.2009.10411921}, 9045 issn = {1559-8608}, 9046 journal = {Journal of Statistical Theory and Practice}, 9047 keywords = {Bayesian network; Fault tree; Imprecise Dirichlet model; Multilevel data; Multinomial-Dirichlet model; Reliability}, 9048 localfile = {article/Wilson-Huzurbazar-Sentz-2009.pdf}, 9049 month = mar, 9050 number = {1}, 9051 pages = {211–223}, 9052 publisher = {Taylor \& Francis}, 9053 title = {The Imprecise Dirichlet Model for Multilevel System Reliability}, 9054 volume = {3}, 9055 year = {2009} 9056 } 9057 9058 @article{deFinetti-1981-BJPS, 9059 author = {Bruno de Finetti}, 9060 doi = {10.1093/bjps}, 9061 journal = {The British Journal for the Philosophy of Science}, 9062 localfile = {article/deFinetti-1981-BJPS.pdf}, 9063 number = {1}, 9064 pages = {55–56}, 9065 publisher = {British Society for the Philosophy of Science}, 9066 title = {The role of `Dutch books' and of `proper scoring rules'}, 9067 url = {http://www.jstor.org/stable/687386}, 9068 volume = {32}, 9069 year = {1981} 9070 } 9071 9072 @article{Fuchs-Neumaier-2009, 9073 abstract = {Robust design optimization methods applied to real life 9074 problems face some major difficulties: How to deal with the estimation of 9075 probability densities when data are sparse, how to cope with high dimensional 9076 problems and how to use valuable information in the form of unformalized expert 9077 knowledge. In this paper we introduce in detail the clouds formalism as a means 9078 to process available uncertainty information reliably, even if limited in amount 9079 and possibly lacking a formal description. This enables a worst-case analysis 9080 with confidence regions of relevant scenarios which can be involved in an 9081 optimization problem formulation for robust design.}, 9082 author = {Martin Fuchs and Arnold Neumaier}, 9083 doi = {10.1080/15598608.2009.10411922}, 9084 issn = {1559-8608}, 9085 journal = {Journal of Statistical Theory and Practice}, 9086 keywords = {Clouds; Confidence regions; Design optimization; Potential clouds; Robust design; Uncertainty modeling}, 9087 localfile = {article/Fuchs-Neumaier-2009.pdf}, 9088 month = mar, 9089 number = {1}, 9090 pages = {225–238}, 9091 publisher = {Taylor \& Francis}, 9092 title = {Potential Based Clouds in Robust Design Optimization}, 9093 volume = {3}, 9094 year = {2009} 9095 } 9096 9097 @article{Walter-Augustin-2009, 9098 abstract = {A great advantage of imprecise probability models over 9099 models based on precise, traditional probabilities is the potential to reflect 9100 the amount of knowledge they stand for. Consequently, imprecise probability 9101 models promise to offer a vivid tool for handling situations of prior-data 9102 conflict in (generalized) Bayesian inference. In this paper we consider a 9103 general class of recently studied imprecise probability models, including the 9104 Imprecise Dirichlet Model under prior information, and more generally the 9105 framework of Quaeghebeur and de Cooman for imprecise inference in canonical 9106 exponential families. We demonstrate that such models, in their originally 9107 proposed form, prove to be insensitive to the extent of prior-data conflict. We 9108 propose an extension reestablishing the natural relationship between knowledge 9109 and imprecision: The higher the discrepancy between the observed sample and what 9110 was expected from prior knowledge, the higher the imprecision in the posterior, 9111 producing cautious inferences if, and only if, caution is needed. Our approach 9112 is illustrated by some examples and simulation results.}, 9113 author = {Gero Walter and Thomas Augustin}, 9114 doi = {10.1080/15598608.2009.10411924}, 9115 issn = {1559-8608}, 9116 journal = {Journal of Statistical Theory and Practice}, 9117 keywords = {Canonical exponential family; Generalized Bayesian inference; Generalized Bayes’ Rule; Imprecise Dirichlet Model (IDM); Imprecise priors; Prior-data conflict; Posterior imprecision; Robust Bayesian analysis}, 9118 localfile = {article/Walter-Augustin-2009.pdf}, 9119 month = mar, 9120 number = {1}, 9121 pages = {255–271}, 9122 publisher = {Taylor \& Francis}, 9123 title = {Imprecision and Prior-Data Conflict in Generalized Bayesian Inference}, 9124 volume = {3}, 9125 year = {2009} 9126 } 9127 9128 @article{Danielson-Ekenberg-Riabacke-2009, 9129 abstract = {Most current decision analytical tools and elicitation 9130 methods are built on the assumption that decision-makers are able to make their 9131 probability and utility assessments in a proper manner. This is, however, often 9132 not the case. The specification and execution of elicitation processes are in 9133 the majority of cases left to the discretion of the users, not least in 9134 user-driven cases such as public information and e-democracy projects. A number 9135 of studies have shown, among other things, that people's natural choice 9136 behaviour deviates from normative assumptions, and that the results display an 9137 inertia gap due to differently framed prospects. One reason for the occurrence 9138 of the inertia gap is people's inability to express their preferences as single 9139 numbers. Instead of considering this as being a human error, this paper uses the 9140 gap in order to develop a class of methods more aligned to the observed 9141 behaviour. The core idea of the class is to acknowledge the existence of the gap 9142 and, as a consequence, not elicit single point numbers.}, 9143 author = {Mats Danielson and Love Ekenberg and Ari Riabacke}, 9144 doi = {10.1080/15598608.2009.10411917}, 9145 issn = {1559-8608}, 9146 journal = {Journal of Statistical Theory and Practice}, 9147 keywords = {Decision analysis; Elicitation method; Imprecise information; Interval assessments}, 9148 localfile = {article/Danielson-Ekenberg-Riabacke-2009.pdf}, 9149 month = mar, 9150 number = {1}, 9151 pages = {157–168}, 9152 publisher = {Taylor \& Francis}, 9153 title = {A Prescriptive Approach to Elicitation of Decision Data}, 9154 volume = {3}, 9155 year = {2009} 9156 } 9157 9158 @article{Strobl-Augustin-2009, 9159 abstract = {Classification and regression trees are a popular and easy 9160 to interpret non-parametric regression approach, but are known to be very 9161 instable: Small changes in the learning sample can produce completely different 9162 trees. Therefore recently it has become state-of-the-art to consider ensembles 9163 (i.e. sets) of trees. The present paper contributes to the so-called TWIX 9164 approach, which produces ensembles by extra splits in additional cutpoints. This 9165 approach can be considered as a compromise between the interpretable but 9166 instable single tree models and the stable but no longer interpretable ensemble 9167 methods bagging and random forests. Based on the idea to study the sensitivity 9168 of a split to some virtual, yet unseen observations, we develop a new, data 9169 driven, cutpoint selection criterion, that technically turns out to be closely 9170 related to an upper entropy approach based on an Imprecise Dirichlet Model. Our 9171 criterion combines several attractive features: By adding extra cutpoints only 9172 iff the underlying cutpoint is instable, the tree is robustified parsimoniously 9173 and the computational expense of the resulting TWIX ensemble is reduced 9174 considerably. As a welcome by-product we moreover obtain a vivid diagnostic 9175 measure for the robustness of a single tree model. The rationale and benefit of 9176 our new adaptive criterion are illustrated by means of a small data example and 9177 a simulation study. Credal classification rules for robust aggregated 9178 predictions from sets of trees are briefly sketched in an outlook.}, 9179 author = {Carolin Strobl and Thomas Augustin}, 9180 doi = {10.1080/15598608.2009.10411915}, 9181 issn = {1559-8608}, 9182 journal = {Journal of Statistical Theory and Practice}, 9183 keywords = {Aggregation; Bagging; C4.5; Classification trees; Credal classification; CART; Cutpoint selection; Imprecise Dirichlet Model; Gini index; Random forests; Shannon entropy; TWIX}, 9184 localfile = {article/Strobl-Augustin-2009.pdf}, 9185 month = mar, 9186 number = {1}, 9187 pages = {119–135}, 9188 publisher = {Taylor \& Francis}, 9189 title = {Adaptive Selection of Extra Cutpoints—Towards Reconciling Robustness and Interpretability in Classification Trees}, 9190 volume = {3}, 9191 year = {2009} 9192 } 9193 9194 @article{Montgomery-Coolen-Hart-2009, 9195 abstract = {Refined risk assessments should increase realism compared 9196 with the first tier deterministic risk assessment. This may involve using 9197 probabilistic methods which account separately for uncertainty and variability. 9198 Analysts use cumulative distribution functions to represent variability, and 9199 bounds around these to illustrate uncertainty. In probability bounds analysis, 9200 parametric probability boxes (p-boxes) are usually formed using intervals for 9201 each parameter. In this paper a Bayesian framework is adopted, which takes 9202 account of dependencies between parameters. Bayesian p-boxes use imprecision 9203 represented by bounds to summarise the uncertainty surrounding the risk 9204 distribution parameters.}, 9205 author = {Victoria J. Montgomery and Frank P. A. Coolen and Andy D. M. Hart}, 9206 doi = {10.1080/15598608.2009.10411912}, 9207 issn = {1559-8608}, 9208 journal = {Journal of Statistical Theory and Practice}, 9209 keywords = {Bayesian methods; Cumulative distribution functions; Highest posterior density regions; Risk assessment; Probability boxes}, 9210 localfile = {article/Montgomery-Coolen-Hart-2009.pdf}, 9211 month = mar, 9212 number = {1}, 9213 pages = {69–83}, 9214 publisher = {Taylor \& Francis}, 9215 title = {Bayesian Probability Boxes in Risk Assessment}, 9216 volume = {3}, 9217 year = {2009} 9218 } 9219 9220 @article{Farrow-Goldstein-2009, 9221 abstract = {We develop methods for analysing decision problems based on 9222 multi-attribute utility hierarchies, structured by mutual utility independence, 9223 which are not precisely specified due to unwillingness or inability of an 9224 individual or group to agree on precise values for the trade-offs between the 9225 various attributes. Instead, our analysis is based on whatever limited 9226 collection of preferences we may assert between attribute collections. These 9227 preferences identify a class of Pareto optimal decisions. We show how to reduce 9228 the class further by combining rules which are almost equivalent and introduce 9229 general principles appropriate to selecting decisions in an imprecise hierarchy. 9230 The approach is illustrated by the design of a university course module.}, 9231 author = {M. Farrow and Michael Goldstein}, 9232 doi = {10.1080/15598608.2009.10411916}, 9233 issn = {1559-8608}, 9234 journal = {Journal of Statistical Theory and Practice}, 9235 keywords = {Imprecise utilities; Mutual utility independence; Pareto optimality; Robust decisions; Utility hierarchies}, 9236 localfile = {article/Farrow-Goldstein-2009.pdf}, 9237 month = mar, 9238 number = {1}, 9239 pages = {137–155}, 9240 publisher = {Taylor \& Francis}, 9241 title = {Almost-Pareto Decision Sets in Imprecise Utility Hierarchies}, 9242 volume = {3}, 9243 year = {2009} 9244 } 9245 9246 @article{Bickis-2009, 9247 abstract = {Given data on inter-arrival times, the imprecise Dirichlet 9248 model can be used to determine upper and lower values on the survival function. 9249 Similar bounds on the hazard function can be quite irregular without some 9250 structural assumptions. To address this problem, a family of prior distributions 9251 for a binomial success probability is contructed by assuming that the logit of 9252 the probability has a normal distribution. Posterior distributions so defined 9253 form a three-dimensional exponential family of which the beta family is a 9254 limiting case. This family is extended to the multivariate case, which provides 9255 for the inclusion of prior information about autocorrelation in the parameters. 9256 By restricting the hyperparameters to a suitably chosen subset, this model is 9257 proposed as an alternative to the usual imprecise Dirichlet model of Walley, 9258 having the advantage of providing smoother estimates of the hazard function. The 9259 methods are applied to data on inter-occurrence times of pandemic influenza.}, 9260 annote = {doi: 10.1080/15598608.2009.10411919}, 9261 author = {Miķelis Bickis}, 9262 doi = {10.1080/15598608.2009.10411919}, 9263 issn = {1559-8608}, 9264 journal = {Journal of Statistical Theory and Practice}, 9265 keywords = {Autocorrelation; Hazard function; Imprecise inference}, 9266 localfile = {article/Bickis-2009.pdf}, 9267 month = mar, 9268 number = {1}, 9269 pages = {183–195}, 9270 publisher = {Taylor \& Francis}, 9271 title = {The Imprecise Logit-Normal Model and its Application to Estimating Hazard Functions}, 9272 volume = {3}, 9273 year = {2009} 9274 } 9275 9276 @incollection{Schempp-1977-Bernstein, 9277 author = {Walter Schempp}, 9278 booktitle = {Constructive Theory of Functions of Several Variables}, 9279 doi = {10.1007/BFb0086576}, 9280 editor = {Walter Schempp and Karl Zeller}, 9281 localfile = {inbook/Schempp-1977-Bernstein.pdf}, 9282 pages = {212–219}, 9283 publisher = {Springer}, 9284 series = {Lecture Notes in Mathematics}, 9285 title = {Bernstein Polynomials in Several Variables}, 9286 volume = {571}, 9287 year = {1977} 9288 } 9289 9290 @article{Crossman-CoolenSchrijner-Coolen-2009, 9291 abstract = {This paper concerns discrete-time time-homogeneous 9292 birth-death processes on a finite state space, containing a single absorbing 9293 state, with interval-valued transition probabilities. As absorption is certain, 9294 the quasi-stationary behaviour of the process is studied with the distribution 9295 of the process conditional on non-absorption. It is shown that the set of all 9296 possible limiting conditional distributions is the set of all possible 9297 quasi-stationary distributions. An approximation of the possibly infinite set of 9298 conditional distributions at time n is presented, together with an example.}, 9299 author = {Richard J. Crossman and Pauline Coolen-Schrijner and Frank P. A. Coolen}, 9300 doi = {10.1080/15598608.2009.10411914}, 9301 issn = {1559-8608}, 9302 journal = {Journal of Statistical Theory and Practice}, 9303 keywords = {Absorbing state; Birth-death process; Interval probability; Limiting conditional distribu- tion; Time-homogeneity; Quasi-stationary distribution}, 9304 localfile = {article/Crossman-CoolenSchrijner-Coolen-2009.pdf}, 9305 month = mar, 9306 number = {1}, 9307 pages = {103–118}, 9308 publisher = {Taylor \& Francis}, 9309 title = {Time-Homogeneous Birth-Death Processes with Probability Intervals and Absorbing State}, 9310 volume = {3}, 9311 year = {2009} 9312 } 9313 9314 @article{Smithson-Segale-2009, 9315 abstract = {On grounds of insufficient reason, a probability of 1/K is 9316 assigned to K mutually exclusive possible events when nothing is known about the 9317 likelihood of those events. Fox and Rottenstreich (2003) present evidence that 9318 subjective probability judgments are typically biased towards this ignorance 9319 prior, and therefore depend on the partition K. Results from two studies 9320 indicate that lower-upper (imprecise) probability judgments by naive judges also 9321 exhibit partition dependence, despite the potential that imprecise probabilities 9322 provide for avoiding it. However, beta regression reveals two kinds of priming 9323 effects, one of which is modeled by mixture distributions. Another novel finding 9324 suggests that when partition primes conflict with a normatively correct 9325 partition some judges widen their probability intervals to encompass both 9326 partitions. The results indicate that imprecise probability judgments may be 9327 better suited than precise probabilities for handling conflicting or ambiguous 9328 information about partitions.}, 9329 author = {Michael Smithson and Carl Segale}, 9330 doi = {10.1080/15598608.2009.10411918}, 9331 issn = {1559-8608}, 9332 journal = {Journal of Statistical Theory and Practice}, 9333 keywords = {Imprecise probability; Judgment; Partition; Subjective probability}, 9334 localfile = {article/Smithson-Segale-2009.pdf}, 9335 month = mar, 9336 number = {1}, 9337 pages = {169–181}, 9338 publisher = {Taylor \& Francis}, 9339 title = {Partition Priming in Judgments of Imprecise Probabilities}, 9340 volume = {3}, 9341 year = {2009} 9342 } 9343 9344 @article{CoolenSchrijner-Maturi-Coolen-2009.pdf, 9345 abstract = {This paper presents a statistical method for comparison of 9346 two groups based on nonparametric predictive inference (NPI). NPI is a 9347 statistical approach based on few modelling assumptions, with inferences 9348 strongly based on data and uncertainty quantified via lower and upper 9349 probabilities. Life- times of units from groups X and Y are compared, based on 9350 observed lifetimes from an experiment that may have ended before all units 9351 failed. We present upper and lower probabilities for the event that the lifetime 9352 of a future unit from X is less than the lifetime of a future unit from Y, and 9353 we compare this approach with traditional precedence testing.}, 9354 author = {Pauline Coolen-Schrijner and Tahani A. Maturi and Frank P. A. Coolen}, 9355 doi = {10.1080/15598608.2009.10411925}, 9356 issn = {1559-8608}, 9357 journal = {Journal of Statistical Theory and Practice}, 9358 keywords = {Lower and upper probabilities; Nonparametric predictive inference; Pairwise comparison; Precedence tests}, 9359 localfile = {article/CoolenSchrijner-Maturi-Coolen-2009.pdf}, 9360 month = mar, 9361 number = {1}, 9362 pages = {273–287}, 9363 publisher = {Taylor \& Francis}, 9364 title = {Nonparametric predictive precedence testing for two groups}, 9365 volume = {3}, 9366 year = {2009} 9367 } 9368 9369 @article{Bose-2009-smoothness, 9370 abstract = {We examine the role of the likelihood in Bayesian robustness 9371 with the density ratio class (DeRobertis and Hartigan, 1981. Ann. Stat.) and 9372 show how to impose smoothness on the density ratio class after imposing shape 9373 constraints. We discuss how to impose shape constraints on the density bounded 9374 class (Lavine, 1991. JASA)}, 9375 annote = {doi: 10.1080/15598608.2009.10411911}, 9376 author = {Sudip Bose}, 9377 doi = {10.1080/15598608.2009.10411911}, 9378 issn = {1559-8608}, 9379 journal = {Journal of Statistical Theory and Practice}, 9380 keywords = {Bayesian robustness; Density bounded; Density ratio; Likelihood; Neighborhood class; Smoothness; Symmetry; Unimodality; Convexity; Minimax; Posterior regret; $\Gamma$-minimax}, 9381 localfile = {article/Bose-2009-smoothness.pdf}, 9382 month = mar, 9383 number = {1}, 9384 pages = {57–67}, 9385 publisher = {Taylor \& Francis}, 9386 title = {On smoothness constraints with shape constraints in a robust Bayesian analysis}, 9387 volume = {3}, 9388 year = {2009} 9389 } 9390 9391 @article{Renooij-VanderGaag-2008-EQPN, 9392 abstract = {Qualitative probabilistic networks were designed to 9393 overcome, to at least some extent, the quantification problem known to 9394 probabilistic networks. Qualitative networks abstract from the numerical 9395 probabilities of their quantitative counterparts by using signs to summarise the 9396 probabilistic influences between their variables. One of the major drawbacks of 9397 these qualitative abstractions, however, is the coarse level of representation 9398 detail that does not provide for indicating strengths of influences. As a 9399 result, the trade-offs modelled in a network remain unresolved upon inference. 9400 We present an enhanced formalism of qualitative probabilistic networks to 9401 provide for a finer level of representation detail. An enhanced qualitative 9402 probabilistic network differs from a basic qualitative network in that it 9403 distinguishes between strong and weak influences. Now, if a strong influence is 9404 combined, upon inference, with a conflicting weak influence, the sign of the net 9405 influence may be readily determined. Enhanced qualitative networks are purely 9406 qualitative in nature, as basic qualitative networks are, yet allow for 9407 resolving some trade-offs upon inference.}, 9408 author = {Silja Renooij and Linda C. van der Gaag}, 9409 doi = {10.1016/j.artint.2008.04.001}, 9410 issn = {0004-3702}, 9411 journal = {Artificial Intelligence}, 9412 keywords = {Probabilistic reasoning; Qualitative reasoning; Trade-off resolution}, 9413 number = {12-13}, 9414 pages = {1470–1494}, 9415 title = {Enhanced qualitative probabilistic networks for resolving trade-offs}, 9416 volume = {172}, 9417 year = {2008} 9418 } 9419 9420 @article{Bolt-VanderGaag-Renooij-2005, 9421 abstract = {A qualitative probabilistic network is a graphical model of 9422 the probabilistic influences among a set of statistical variables, in which each 9423 influence is associated with a qualitative sign. A non-monotonic influence 9424 between two variables is associated with the ambiguous sign ‘?’, which indicates 9425 that the actual sign of the influence depends on the state of the network. The 9426 presence of such ambiguous signs is undesirable as it tends to lead to 9427 uninformative results upon inference. In this paper, we argue that, although a 9428 non-monotonic influence may have varying effects, in each specific state of the 9429 network, its effect is unambiguous. To capture the current effect of the 9430 influence, we introduce the concept of situational sign. We show how situational 9431 signs can be used upon inference and how they are updated as the state of the 9432 network changes. By means of a real-life qualitative network in oncology, we 9433 show that the use of situational signs can effectively forestall uninformative 9434 results upon inference.}, 9435 author = {Janneke H. Bolt and Linda C. van der Gaag and Silja Renooij}, 9436 doi = {10.1016/j.ijar.2004.05.009}, 9437 issn = {0888-613X}, 9438 journal = {International Journal of Approximate Reasoning}, 9439 number = {3}, 9440 pages = {333–354}, 9441 title = {Introducing situational signs in qualitative probabilistic networks}, 9442 volume = {38}, 9443 year = {2005} 9444 } 9445 9446 @article{Renooij-VanderGaag-Parsons-2002, 9447 abstract = {Qualitative probabilistic networks are qualitative 9448 abstractions of probabilistic networks, summarising probabilistic influences by 9449 qualitative signs. As qualitative networks model influences at the level of 9450 variables, knowledge about probabilistic influences that hold only for specific 9451 values cannot be expressed. The results computed from a qualitative network, as 9452 a consequence, can be weaker than strictly necessary and may in fact be rather 9453 uninformative. We extend the basic formalism of qualitative probabilistic 9454 networks by providing for the inclusion of context-specific information about 9455 influences and show that exploiting this information upon reasoning has the 9456 ability to forestall unnecessarily weak results.}, 9457 author = {Silja Renooij and Linda C. van der Gaag and Simon Parsons}, 9458 doi = {10.1016/S0004-3702(02)00247-3}, 9459 issn = {0004-3702}, 9460 journal = {Artificial Intelligence}, 9461 keywords = {Probabilistic reasoning; Qualitative reasoning; Context-specific independence; Non-monotonicity}, 9462 number = {1-2}, 9463 pages = {207–230}, 9464 title = {Context-specific sign-propagation in qualitative probabilistic networks}, 9465 volume = {140}, 9466 year = {2002} 9467 } 9468 9469 @inproceedings{Renooij-VanderGaag-2002-UAI, 9470 address = {San Francisco, California}, 9471 author = {Silja Renooij and Linda C. van der Gaag}, 9472 booktitle = {UAI-02: Proceedings of the Eighteenth Conference on Uncertainty in Artificial Intelligence}, 9473 pages = {422–429}, 9474 publisher = {Morgan Kaufmann}, 9475 title = {From qualitative to quantitative probabilistic networks}, 9476 year = {2002} 9477 } 9478 9479 @article{Renooij-VanderGaag-2000-IPMU, 9480 author = {Silja Renooij and Linda C. van der Gaag}, 9481 booktitle = {IPMU 2000: Proceedings of the Eighth International Conference on Information Processing and Management of Uncertainty in Knowledge-based Systems}, 9482 location = {Madrid}, 9483 pages = {1285–1290}, 9484 title = {Exploiting non-monotonic influences in qualitative belief networks}, 9485 year = {2000} 9486 } 9487 9488 @article{Wellman-1990-QPN, 9489 abstract = {Graphical representations for probabilistic relationships 9490 have recently received considerable attention in AI. Qualitative probabilistic 9491 networks abstract from the usual numeric representations by encoding only 9492 qualitative relationships, which are inequality constraints on the joint 9493 probability distribution over the variables. Although these constraints are 9494 insufficient to determine probabilities uniquely, they are designed to justify 9495 the deduction of a class of relative likelihood conclusions that imply useful 9496 decision-making properties. Two types of qualitative relationship are defined, 9497 each a probabilistic form of monotonicity constraint over a group of variables. 9498 Qualitative influences describe the direction of the relationship between two 9499 variables. Qualitative synergies describe interactions among influences. The 9500 probabilistic definitions chosen justify sound and efficient inference 9501 procedures based on graphical manipulations of the network. These procedures 9502 answer queries about qualitative relationships among variables separated in the 9503 network and determine structural properties of optimal assignments to decision 9504 variables.}, 9505 author = {Michael P. Wellman}, 9506 doi = {10.1016/0004-3702(90)90026-V}, 9507 issn = {0004-3702}, 9508 journal = {Artificial Intelligence}, 9509 number = {3}, 9510 pages = {257–303}, 9511 title = {Fundamental concepts of qualitative probabilistic networks}, 9512 volume = {44}, 9513 year = {1990} 9514 } 9515 9516 @article{Steeneveld-etal-2010, 9517 abstract = {Automatic milking systems (AMS) generate alert lists 9518 reporting cows likely to have clinical mastitis (CM). Dutch farmers indicated 9519 that they use non-AMS cow information or the detailed alert information from the 9520 AMS to decide whether to check an alerted cow for CM. However, it is not yet 9521 known to what extent such information can be used to discriminate between 9522 true-positive and false-positive alerts. The overall objective was to 9523 investigate whether selection of the alerted cows that need further 9524 investigation for CM can be made. For this purpose, non-AMS cow information and 9525 detailed alert information were used. During a 2-yr study period, 11,156 alerts 9526 for CM, including 159 true-positive alerts, were collected at one farm in the 9527 Netherlands. Non-AMS cow information on parity, days in milk, season of the 9528 year, somatic cell count history, and CM history was added to each alert. In 9529 addition, 6 alert information variables were defined. These were the height of 9530 electrical conductivity, the alert origin (electrical conductivity, color, or 9531 both), whether or not a color alert for mastitic milk was given, whether or not 9532 a color alert for abnormal milk was given, deviation from the expected milk 9533 yield, and the number of alerts of the cow in the preceding 12 to 96\&\#xa0;h. 9534 Subsequently, naive Bayesian networks (NBN) were constructed to compute the 9535 posterior probability of an alert being truly positive based only on non-AMS cow 9536 information, based on only alert information, or based on both types of 9537 information. The NBN including both types of information had the highest area 9538 under the receiver operating characteristic curve (AUC; 0.78), followed by the 9539 NBN including only alert information (AUC\&\#xa0;=\&\#xa0;0.75) and the NBN 9540 including only non-AMS cow information (AUC\&\#xa0;=\&\#xa0;0.62). By combining 9541 the 2 types of information and by setting a threshold on the computed 9542 probabilities, the number of false-positive alerts on a mastitis alert list was 9543 reduced by 35\%, and 10\% of the true-positive alerts would not be identified. 9544 To detect CM cases at a farm with an AMS, checking all alerts is still the best 9545 option but would result in a high workload. Checking alerts based on a single 9546 alert information variable would result in missing too many true-positive cases. 9547 Using a combination of alert information variables, however, is the best way to 9548 select cows that need further investigation. The effect of adding non-AMS cow 9549 information on making a distinction between true-positive and false-positive 9550 alerts would be minor.}, 9551 author = {W. Steeneveld and Linda C. van der Gaag and W. Ouweltjes and H. Mollenhorst and H. Hogeveen}, 9552 doi = {10.3168/jds.2009-3020}, 9553 issn = {0022-0302}, 9554 journal = {Journal of Dairy Science}, 9555 keywords = {clinical mastitis; detection; automatic milking; dairy cow}, 9556 number = {6}, 9557 pages = {2559–2568}, 9558 title = {Discriminating between true-positive and false-positive clinical mastitis alerts from automatic milking systems}, 9559 volume = {93}, 9560 year = {2010} 9561 } 9562 9563 @inproceedings{TabachneckSchijf-etal-2008, 9564 author = {Hermi J. M. Tabachneck-Schijf and Linda C. van der Gaag and Petra L. Geenen and Martijn M. Schrage and W. L. A. Loeffen and A. R. W. Elbers}, 9565 booktitle = {Proceedings of the 20th International Pig Veterinary Science Congress}, 9566 editor = {P. Evans}, 9567 location = {Durban, South Africa}, 9568 title = {Designing a personal digital assistant for early on-site detection of classical swine fever in a pig unit}, 9569 year = {2008} 9570 } 9571 9572 @inproceedings{Geenen-VanderGaag-2005, 9573 author = {Petra L. Geenen and Linda C. van der Gaag}, 9574 booktitle = {Proceedings of the Third Bayesian Modelling Applications Workshop}, 9575 location = {Edinburgh}, 9576 title = {Developing a Bayesian network for clinical diagnosis in veterinary medicine: from the individual to the herd}, 9577 year = {2005} 9578 } 9579 9580 @article{Grunwald-Halpern-2011, 9581 author = {Peter D. Grünwald and Joseph Y. Halpern}, 9582 doi = {10.1613/jair.3374}, 9583 journal = {Journal of Artificial Intelligence Research}, 9584 pages = {393–426}, 9585 title = {Making decisions using sets of probabilities: updating, time consistency, and calibration.}, 9586 volume = 42, 9587 year = 2011 9588 } 9589 9590 @book{Pourret-Naim-Marcot-2008, 9591 editor = {Olivier Pourret and Patrick Naïm and Bruce Marcot}, 9592 isbn = {978-0-470-06030-8}, 9593 publisher = {Wiley}, 9594 title = {Bayesian networks: a practical guide to applications}, 9595 year = {2008} 9596 } 9597 9598 @inproceedings{VanderGaag-1990, 9599 abstract = {Many AI researchers argue that probability theory is only 9600 capable of dealing with uncertainty in situations where a full specification of 9601 a joint probability distribution is available, and conclude that it is not 9602 suitable for application in knowledge-based systems. Probability intervals, 9603 however, constitute a means for expressing incompleteness of information. We 9604 present a method for computing such probability intervals for probabilities of 9605 interest from a partial specification of a joint probability distribution. Our 9606 method improves on earlier approaches by allowing for independency relationships 9607 between statistical variables to be exploited.}, 9608 address = {Amsterdam, the Netherlands}, 9609 author = {Linda C. van der Gaag}, 9610 booktitle = {UAI-90: Proceedings of the Sixth Conference on Uncertainty in Artificial Intelligence}, 9611 pages = {457–466}, 9612 publisher = {Elsevier}, 9613 title = {Computing Probability Intervals Under Independency Constraints}, 9614 year = {1990} 9615 } 9616 9617 @inproceedings{VanderGaag-etal-1999, 9618 abstract = {In building Bayesian belief networks, the elicitation of all 9619 probabilities required can be a major obstacle. We learned the extent of this 9620 often-cited observation in the construction of the probabilistic part of a 9621 complex influence diagram in the field of cancer treatment. Based upon our 9622 negative experiences with existing methods, we designed a new method for 9623 probability elicitation from domain experts. The method combines various ideas, 9624 among which are the ideas of transcribing probabilities and of using a scale 9625 with both numerical and verbal anchors for marking assessments. In the 9626 construction of the probabilistic part of our influence diagram, the method 9627 proved to allow for the elicitation of many probabilities in little time.}, 9628 address = {San Francisco, California}, 9629 author = {Linda C. van der Gaag and Silja Renooij and Cilia L. M. Witteman and Berthe M. P. Aleman and Babs G. Taal}, 9630 booktitle = {UAI-99: Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence}, 9631 keywords = {belief networks; expert elicitation}, 9632 pages = {647–654}, 9633 publisher = {Morgan Kaufmann}, 9634 title = {How to elicit many probabilities}, 9635 year = {1999} 9636 } 9637 9638 @article{VanderGaag-etal-2002, 9639 abstract = {With the help of two experts in gastrointestinal oncology 9640 from The Netherlands Cancer Institute, Antoni van Leeuwenhoekhuis, a 9641 decision-support system is being developed for patient-specific therapy 9642 selection for oesophageal cancer. The kernel of the system is a probabilistic 9643 network that describes the presentation characteristics of cancer of the 9644 oesophagus and the pathophysiological processes of invasion and metastasis. 9645 While the construction of the graphical structure of the network was relatively 9646 straightforward, probability elicitation with existing methods proved to be a 9647 major obstacle. To overcome this obstacle, we designed a new method for 9648 eliciting probabilities from experts that combines the ideas of transcribing 9649 probabilities as fragments of text and of using a scale with both numerical and 9650 verbal anchors for marking assessments. In this paper, we report experiences 9651 with our method in eliciting the probabilities required for the oesophagus 9652 network. The method allowed us to elicit many probabilities in reasonable time. 9653 To gain some insight in the quality of the probabilities obtained, we conducted 9654 a preliminary evaluation study of our network, using data from real patients. We 9655 found that for 85\% of the patients, the network predicted the correct cancer 9656 stage.}, 9657 author = {Linda C. van der Gaag and Silja Renooij and Cilia L. M. Witteman and Berthe M. P. Aleman and Babs G. Taal}, 9658 doi = {10.1016/S0933-3657(02)00012-X}, 9659 issn = {0933-3657}, 9660 journal = {Artificial Intelligence in Medicine}, 9661 keywords = {Elicitation of judgemental probabilities; Probabilistic networks}, 9662 number = {2}, 9663 pages = {123–148}, 9664 title = {Probabilities for a probabilistic network: a case study in oesophageal cancer}, 9665 volume = {25}, 9666 year = {2002} 9667 } 9668 9669 @inproceedings{Helsper-VanderGaag-Groenendaal-2004, 9670 author = {E. Helsper and Linda C. van der Gaag and F. Groenendaal}, 9671 booktitle = {Engineering Knowledge in the Age of the Semantic Web}, 9672 editor = {E. Motta and N. R. Shadbolt and A. Stutt and N. Gibbins}, 9673 pages = {280–292}, 9674 publisher = {Springer}, 9675 title = {Designing a procedure for the acquisition of probability constraints for Bayesian networks}, 9676 year = {2004} 9677 } 9678 9679 @article{Sent-etal-2005, 9680 author = {D. Sent and Linda C. van der Gaag and Cilia L. M. Witteman and Berthe M. P. Aleman and Babs G. Taal}, 9681 journal = {Interdisciplinary Journal of Artificial Intelligence and the Simulation of Behaviour}, 9682 number = {6}, 9683 pages = {543–561}, 9684 title = {Eliciting test-selection strategies for a decision-support system in oncology}, 9685 volume = {1}, 9686 year = {2005} 9687 } 9688 9689 @inproceedings{Geenen-etal-2006, 9690 author = {Petra L. Geenen and A. R. W. Elbers and Linda C. van der Gaag and W. L. A. Loeffen}, 9691 booktitle = {Proceedings of the Eleventh Symposium of the International Society for Veterinary Epidemiology and Economics}, 9692 pages = {667–669}, 9693 title = {Development of a probabilistic network for clinical detection of classical swine fever}, 9694 year = {2006} 9695 } 9696 9697 @article{Laskey-1995, 9698 abstract = {When eliciting a probability model from experts, knowledge 9699 engineers may compare the results of the model with expert judgment on test 9700 scenarios, then adjust model parameters to bring the behavior of the model more 9701 in line with the experts intuition. This paper presents a methodology for 9702 analytic computation of sensitivity values in Bayesian network models. 9703 Sensitivity values are partial derivatives of output probabilities with respect 9704 to parameters being varied in the sensitivity analysis. They measure the impact 9705 of small changes in a network parameter on a target probability value or 9706 distribution. Sensitivity values can be used to focus knowledge elicitation 9707 effort on those parameters having the most impact on outputs of concern. 9708 Analytic sensitivity values are computed for an example and compared to 9709 sensitivity analysis by direct variation of parameters}, 9710 author = {K. B. Laskey}, 9711 doi = {10.1109/21.384252}, 9712 issn = {0018-9472}, 9713 journal = {IEEE Transactions on Systems, Man and Cybernetics}, 9714 keywords = {Bayesian networks; knowledge elicitation; knowledge engineering; probability assessments; sensitivity analysis; symbolic reasoning; target probability value; uncertainty representation; Bayes methods; inference mechanisms; knowledge acquisition; probability; sensitivity analysis}, 9715 month = jun, 9716 number = {6}, 9717 pages = {901–909}, 9718 title = {Sensitivity analysis for probability assessments in Bayesian networks}, 9719 volume = {25}, 9720 year = {1995} 9721 } 9722 9723 @inproceedings{Chan-Darwiche-2004, 9724 abstract = {Previous work on sensitivity analysis in Bayesian networks 9725 has focused on single parameters, where the goal is to understand the 9726 sensitivity of queries to single parameter changes, and to identify single 9727 parameter changes that would enforce a certain query constraint. In this paper, 9728 we expand the work to multiple parameters which may be in the CPT of a single 9729 variable, or the CPTs of multiple variables. Not only do we identify the 9730 solution space of multiple parameter changes that would be needed to enforce a 9731 query constraint, but we also show how to find the optimal solution, that is, 9732 the one which disturbs the current probability distribution the least (with 9733 respect to a specific measure of disturbance). We characterize the computational 9734 complexity of our new techniques and discuss their applications to developing 9735 and debugging Bayesian networks, and to the problem of reasoning about the value 9736 (reliability) of new information.}, 9737 address = {Arlington, Virginia}, 9738 author = {Hei Chan and Adnan Darwiche}, 9739 booktitle = {UAI-04: Proceedings of the Twentieth Conference on Uncertainty in Artificial Intelligence}, 9740 pages = {67–75}, 9741 publisher = {AUAI Press}, 9742 title = {Sensitivity analysis in Bayesian networks: from single to multiple parameters}, 9743 year = {2004} 9744 } 9745 9746 @misc{BNatWork, 9747 author = {BN@Work}, 9748 title = {European Community for Researchers on Probabilistic Graphical Models}, 9749 url = {http://www.bnatwork.org} 9750 } 9751 9752 @misc{SIKS, 9753 author = {SIKS}, 9754 title = {Netherlands research school for Information and Knowledge Systems}, 9755 url = {http://www.siks.nl} 9756 } 9757 9758 @misc{AUAI, 9759 author = {AUAI}, 9760 title = {Association for Uncertainty in Artificial Intelligence}, 9761 url = {http://www.auai.org} 9762 } 9763 9764 @misc{ECCAI, 9765 author = {ECCAI}, 9766 title = {European Coordinating Committee for Artificial Intelligence}, 9767 url = {http://www.eccai.org} 9768 } 9769 9770 @misc{SIPTA, 9771 author = {SIPTA}, 9772 title = {Society for Imprecise Probability: Theories and Applications}, 9773 url = {http://www.sipta.org} 9774 } 9775 9776 @inproceedings{Blanco-etal-2004, 9777 author = {Rosa Blanco and Linda C. van der Gaag and Iñaki Inza and Pedro Larrañaga}, 9778 booktitle = {ISBMDA 2004: Proceedings of the 5th International Symposium on Biological and Medical Data Analysis}, 9779 editor = {José María Barreiro and Fernando Martín-Sánchez and Victor Maojo and Ferran Sanz}, 9780 isbn = {3-540-23964-2}, 9781 pages = {212–223}, 9782 publisher = {Springer}, 9783 series = {Lecture Notes in Computer Science}, 9784 title = {Selective classifiers can be too restrictive: a case-study in oesophageal cancer}, 9785 volume = {3337}, 9786 year = {2004} 9787 } 9788 9789 @article{Feelders-VanderGaag-2006, 9790 abstract = {We consider the problem of learning the parameters of a 9791 Bayesian network from data, while taking into account prior knowledge about the 9792 signs of influences between variables. Such prior knowledge can be readily 9793 obtained from domain experts. We show that this problem of parameter learning is 9794 a special case of isotonic regression and provide a simple algorithm for 9795 computing isotonic estimates. Our experimental results for a small Bayesian 9796 network in the medical domain show that taking prior knowledge about the signs 9797 of influences into account leads to an improved fit of the true distribution, 9798 especially when only a small sample of data is available. More importantly, 9799 however, the isotonic estimator provides parameter estimates that are consistent 9800 with the specified prior knowledge, thereby resulting in a network that is more 9801 likely to be accepted by experts in its domain of application.}, 9802 author = {Ad Feelders and Linda C. van der Gaag}, 9803 doi = {10.1016/j.ijar.2005.10.003}, 9804 issn = {0888-613X}, 9805 journal = {International Journal of Approximate Reasoning}, 9806 keywords = {Bayesian networks; Parameter learning; Order-constrained estimation}, 9807 number = {1-2}, 9808 pages = {37–53}, 9809 title = {Learning Bayesian network parameters under order constraints}, 9810 volume = {42}, 9811 year = {2006} 9812 } 9813 9814 @inproceedings{VanderGaag-etal-2009, 9815 author = {Linda C. van der Gaag and Silja Renooij and Ad Feelders and Arend de Groote and Marinus J. C. Eijkemans and Frank J. Broekmans and Bart C. J. M. Fauser}, 9816 booktitle = {Machine Learning and Data Mining in Pattern Recognition}, 9817 doi = {10.1007/978-3-642-03070-3_59}, 9818 editor = {Petra Perner}, 9819 isbn = {978-3-642-03069-7}, 9820 pages = {787–801}, 9821 publisher = {Springer}, 9822 series = {Lecture Notes in Computer Science}, 9823 title = {Aligning Bayesian Network Classifiers with Medical Contexts.}, 9824 volume = 5632, 9825 year = 2009 9826 } 9827 9828 @incollection{Chateauneuf-Jaffray-1995, 9829 abstract = {The concept of local Möbius transform of a capacity is 9830 introduced and shown to provide a handier characterization of K-monotonicity 9831 than the standard Möbius transformation. It is moreover used to give a new proof 9832 of the preservation of K monotonicity by conditional lower probabilities.}, 9833 author = {Alain Chateauneuf and Jean-Yves Jaffray}, 9834 booktitle = {Symbolic and Quantitative Approaches to Reasoning and Uncertainty}, 9835 doi = {10.1007/3-540-60112-0_14}, 9836 editor = {Christine Froidevaux and Jürg Kohlas}, 9837 isbn = {978-3-540-60112-8}, 9838 localfile = {inbook/Chateauneuf-Jaffray-1995.pdf}, 9839 number = {1}, 9840 pages = {115–124}, 9841 publisher = {Springer}, 9842 series = {Lecture Notes in Computer Science}, 9843 title = {Local Möbius transforms of monotone capacities}, 9844 volume = {946}, 9845 year = {1995} 9846 } 9847 9848 @inproceedings{Quaeghebeur-Shariatmadar-DeCooman-2010-FLINS, 9849 abstract = {We investigate a constrained optimization problem for which 9850 there is uncertainty about a constraint parameter. Our aim is to reformulate it 9851 as a (constrained) optimization problem without uncertainty. This is done by 9852 recasting the original problem as a decision problem under uncertainty. We give 9853 results for a number of different types of uncertainty models—linear and vacuous 9854 previsions, and possibility distributions—and for two different optimality 9855 criteria for decision problems under uncertainty—maximinity and maximality.}, 9856 address = {Singapore}, 9857 author = {Erik Quaeghebeur and Keivan Shariatmadar and Gert {De Cooman}}, 9858 booktitle = {Computational intelligence: foundations and applications: proceedings of the 9th international FLINS conference}, 9859 editor = {Da Ruan and Yianrui Li and Yang Xu and Guoqing Chen and Etienne E. Kerre}, 9860 keywords = {possibility distribution; linear prevision; maximinity; maximality; vacuous prevision; constrained optimization}, 9861 location = {Chengdu, China}, 9862 pages = {791–796}, 9863 publisher = {World Scientific}, 9864 series = {World Scientific Proceedings Series on Computer Engineering and Information Science}, 9865 title = {A constrained optimization problem under uncertainty}, 9866 year = {2010} 9867 } 9868 9869 @article{Quaeghebeur-Shariatmadar-DeCooman-2012-FSS, 9870 author = {Erik Quaeghebeur and Keivan Shariatmadar and Gert {De Cooman}}, 9871 journal = {Fuzzy Sets and Systems}, 9872 title = {Constrained optimization problems under uncertainty with coherent lower previsions}, 9873 year = {submitted} 9874 } 9875 9876 @article{Charnes-Cooper-1959, 9877 abstract = {A new conceptual and analytical vehicle for problems of 9878 temporal planning under uncertainty, involving determination of optimal 9879 (sequential) stochastic decision rules is defined and illustrated by means of a 9880 typical industrial example. The paper presents a method of attack which splits 9881 the problem into two non-linear (or linear) programming parts, (i) determining 9882 optimal probability distributions, (ii) approximating the optimal distributions 9883 as closely as possible by decision rules of prescribed form.}, 9884 author = {A. Charnes and W. W. Cooper}, 9885 doi = {10.1287/mnsc.6.1.73}, 9886 issn = {0025-1909}, 9887 journal = {Management Science}, 9888 localfile = {article/Charnes-Cooper-1959.pdf}, 9889 month = {oct}, 9890 number = {1}, 9891 pages = {73–79}, 9892 publisher = {INFORMS}, 9893 title = {Chance-constrained programming}, 9894 url = {http://www.jstor.org/stable/2627476}, 9895 volume = {6}, 9896 year = {1959} 9897 } 9898 9899 @article{Dantzig-1955, 9900 author = {George B. Dantzig}, 9901 doi = {10.1287/mnsc.1.3-4.197}, 9902 issn = {0025-1909}, 9903 journal = {Management Science}, 9904 localfile = {article/Dantzig-1955.pdf}, 9905 number = {3/4}, 9906 pages = {197–206}, 9907 publisher = {INFORMS}, 9908 title = {Linear Programming under Uncertainty}, 9909 url = {http://www.jstor.org/stable/2627159}, 9910 volume = {1}, 9911 year = {1955} 9912 } 9913 9914 @article{Yu-Zeleny-1975, 9915 abstract = {In this note we are interested in the properties of, and 9916 methods for locating the set of all nondominated solutions of multiple linear 9917 criteria defined over a polyhedron. We first show that the set of all dominated 9918 solutions is convex and that the set of all nondominated solutions is a subset 9919 of the convex hull of the nondominated extreme points. When the domination cone 9920 is polyhedral, we derive a necessary and sufficient condition for a point to be 9921 nondominated. The condition is stronger than that of Ref. [1] and enables us to 9922 give a simple proof that the set of all nondominated extreme points indeed is 9923 connected. In order to locate the entire set of all nondominated extreme points, 9924 we derive a generalized version of simplex method—multicriteria simplex method. 9925 In addition to some useful results, a necessary and sufficient condition for an 9926 extreme point to be nondominated is derived. Examples and computer experience 9927 are also given. Finally, we focus on how to generate the entire set of all 9928 nondominated solutions through the set of all nondominated extreme points. A 9929 decomposition theorem and some necessary and sufficient conditions for a face to 9930 be nondominated are derived. We then describe a systematic way to identify the 9931 entire set of all nondominated solutions. Through examples, we show that in fact 9932 our procedure is quite efficient.}, 9933 author = {P. L. Yu and M. Zeleny}, 9934 doi = {10.1016/0022-247X(75)90189-4}, 9935 issn = {0022-247X}, 9936 journal = {Journal of Mathematical Analysis and Applications}, 9937 number = {2}, 9938 pages = {430–468}, 9939 title = {The set of all nondominated solutions in linear cases and a multicriteria simplex method}, 9940 volume = {49}, 9941 year = {1975} 9942 } 9943 9944 @article{Evans-Steuer-1973, 9945 abstract = {For linear multiple-objective problems, a necessary and 9946 sufficient condition for a point to be efficient is employed in the development 9947 of a revised simplex algorithm for the enumeration of the set of efficient 9948 extreme points. Five options within this algorithm were tested on a variety of 9949 problems. Results of these tests provide indications for effective use of the 9950 algorithm.}, 9951 author = {J. P. Evans and R. E. Steuer}, 9952 doi = {10.1007/BF01580111}, 9953 issn = {0025-5610}, 9954 journal = {Mathematical Programming}, 9955 pages = {54–72}, 9956 publisher = {Springer Berlin / Heidelberg}, 9957 title = {A revised simplex method for linear multiple objective programs}, 9958 volume = {5}, 9959 year = {1973} 9960 } 9961 9962 @book{Dubois-Prade-1988-en, 9963 address = {New York}, 9964 author = {Didier Dubois and Henri Prade}, 9965 publisher = {Plenum Press}, 9966 title = {Possibility Theory: An Approach to Computerized Processing of Uncertainty}, 9967 year = {1988} 9968 } 9969 9970 @inproceedings{Huntley-etal-2012-FLINS, 9971 abstract = {We present a software implementation of the methods for 9972 solving linear programming problems under uncertainty from previous work. 9973 Uncertainties about constraint parameters can be expressed as intervals or 9974 trapezoidal possibility distributions. The software computes the solutions for 9975 the optimality criteria maximin and maximality. For maximality with possibility 9976 distributions, only an approximate solution is obtained.}, 9977 author = {Nathan Huntley and Rolando Quiñones and Keivan Shariatmadar and Erik Quaeghebeur and Gert {De Cooman} and Etienne E. Kerre}, 9978 keywords = {linear programming; uncertainty; maximin; maximality; implementation}, 9979 note = {Submitted to FLINS 2012}, 9980 title = {Implementation of maximin and maximal solutions for linear programming problems under uncertainty}, 9981 year = {2012} 9982 } 9983 9984 @inproceedings{Quaeghebeur-etal-2012-IPMU, 9985 abstract = {We consider linear programming problems with uncertain 9986 constraint coefficients described by intervals or, more generally, possibility 9987 distributions. The uncertainty is given a behavioral interpretation using 9988 coherent lower previsions from the theory of imprecise probabilities. We give a 9989 meaning to the linear programming problems by reformulating them as decision 9990 problems under such imprecise-probabilistic uncertainty. We provide expressions 9991 for and illustrations of the maximin and maximal solutions of these decision 9992 problems and present computational approaches for dealing with them.}, 9993 author = {Erik Quaeghebeur and Nathan Huntley and Keivan Shariatmadar and Gert {De Cooman}}, 9994 keywords = {linear program; interval uncertainty; vacuous lower prevision; possibility distribution; coherent lower prevision; imprecise probabilities; decision making; maximinity; maximality}, 9995 note = {Submitted to IPMU 2012}, 9996 title = {Maximin and Maximal Solutions for Linear Programming Problems with Possibilistic Uncertainty}, 9997 year = {2012} 9998 } 9999 10000 @book{Dantzig-Thapa-2003, 10001 author = {George B. Dantzig and Mukund N. Thapa}, 10002 booktitle = {Linear Programming:2: Theory and Extensions}, 10003 doi = {10.1007/b97283}, 10004 localfile = {book/Dantzig-Thapa-2003.pdf}, 10005 publisher = {Springer}, 10006 series = {Springer Series in Operations Research}, 10007 year = {2003} 10008 } 10009 10010 @inproceedings{Bagnara-etal-2002, 10011 author = {Roberto Bagnara and Elisa Ricci and Enea Zaffanella and Patricia M. Hill}, 10012 booktitle = {Static Analysis: Proceedings of the 9th International Symposium}, 10013 doi = {10.1007/3-540-45789-5_17}, 10014 editor = {Manuel V. Hermenegildo and Germán Puebla}, 10015 isbn = {3-540-44235-9}, 10016 localfile = {inproceedings/Bagnara-etal-2002.pdf}, 10017 pages = {213–229}, 10018 publisher = {Springer}, 10019 series = {Lecture Notes in Computer Science}, 10020 title = {Possibly Not Closed Convex Polyhedra and the Parma Polyhedra Library.}, 10021 url = {http://bugseng.com/products/ppl/documentation/BagnaraRZH02.pdf}, 10022 volume = 2477, 10023 year = 2002 10024 } 10025