International Symposium on Imprecise Probabilities and Their Applications最新文献

{"title":"Markov Conditions and Factorization in Logical Credal Networks","authors":"Fabio Gagliardi Cozman","doi":"10.48550/arXiv.2302.14146","DOIUrl":"https://doi.org/10.48550/arXiv.2302.14146","url":null,"abstract":"We examine the recently proposed language of Logical Credal Networks, in particular investigating the consequences of various Markov conditions. We introduce the notion of structure for a Logical Credal Network and show that a structure without directed cycles leads to a well-known factorization result. For networks with directed cycles, we analyze the differences between Markov conditions, factorization results, and specification requirements.","PeriodicalId":377089,"journal":{"name":"International Symposium on Imprecise Probabilities and Their Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128702033","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Shape of Incomplete Preferences","authors":"R. Nau","doi":"10.1214/009053606000000740","DOIUrl":"https://doi.org/10.1214/009053606000000740","url":null,"abstract":"Incomplete preferences provide the epistemic foundation for models of imprecise subjective probabilities and utilities that are used in robust Bayesian analysis and in theories of bounded rationality. This paper presents a simple axiomatization of incomplete preferences and characterizes the shape of their representing sets of probabilities and utilities. Deletion of the completeness assumption from the axiom system of Anscombe and Aumann yields preferences represented by a convex set of state-dependent expected utilities, of which at least one must be a probability/utility pair. A strengthening of the state-independence axiom is needed to obtain a representation purely in terms of a set of probability/utility pairs.","PeriodicalId":377089,"journal":{"name":"International Symposium on Imprecise Probabilities and Their Applications","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121513054","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Imprecise and Indeterminate Probabilities","authors":"I. Levi","doi":"10.1017/S1357530900000119","DOIUrl":"https://doi.org/10.1017/S1357530900000119","url":null,"abstract":"Abstract Bayesian advocates of expected utility maximizationuse sets of probability distributions to representvery different ideas. Strict Bayesians insist thatprobability judgment is numerically determinateeven though the agent can represent such judgmentsonly in imprecise terms. According to QuasiBayesians rational agents may make indeterminatesubjective probability judgments. Both kinds ofBayesians require that admissible options maximizeexpected utility according to some probabilitydistribution. Quasi Bayesians permit thedistribution to vary with the context of choice.Maximalists allow for choices that do not maximizeexpected utility against any distribution.Maximiners mandate what maximalists allow. Thispaper defends the quasi Bayesian view against strictBayesians on the one hand and maximalists andmaximiners on the other.Keywords. Strict Bayesian, Quasi Bayesian, E -admissibility, E -maximality , Maximizing lowerexpectation. 1 Introduction Suppose that decision-maker X judges that hisavailable options belong to set S. Set S is itself asubset of a set M (Ω) of probability mixtures of afinite subsets of Ω. X's values, goals and beliefscommit him somehow to an evaluation of theelements of M (Ω) as better or worse. Thisevaluation is representable (by us and notnecessarily by X) by a set of weak orderings ofM (Ω) satisfying the requirements imposed by vonNeumann and Morgenstern on the evaluation oflotteries. Each of these weak orderings isrepresentable by a utility function unique up to apositive affine transformation. Consequently wecan define the value structure V [M (Ω)] to be the setof such permissible utility functions or thepermissible von Neumann-Morgenstern preferencesthey represent.For any finite nonempty subset S of M (Ω), V (S) isthe set of restrictions of the members of V [M (Ω)] tothe domain S. This is the value structure for S and itconsists of permissible utility functions for S. Thus,the value structure V [M (Ω)] determines what thevalue structure V (S) would be were S the set ofoptions X judged to be available to him in a givensituation.Let H be a set of propositions such that the decision-maker is sure that exactly one element of H is true.Moreover, if the decision maker X adds anyproposition s asserting that some option in S isgoing to be implemented to what he is certain istrue, the result is consistent with each and everyelement of H .Let O represent possible outcomes of implementingone or another of the available options in S. Thepropositions characterizing such outcomes specifyinformation X cares about according to his goalsand values. The deductive consequences of X'sbody of certainties K and the assumption that s isimplemented while state h in H is true entails thatexactly one consequence in O is true. This is so foreach s and each H .The extended value structure EV (O ) is representableby a set of utility functions defined for elements ofO . Each of these utility functions may be extendedto the set M (O ) of all mixture","PeriodicalId":377089,"journal":{"name":"International Symposium on Imprecise Probabilities and Their Applications","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122881717","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Human Judgment under Sample Space Ignorance","authors":"M. Smithson, Thomas Bartos, K. Takemura","doi":"10.1017/S1357530900000144","DOIUrl":"https://doi.org/10.1017/S1357530900000144","url":null,"abstract":"This paper surveys results of a research program investigating human judgments of imprecise probabilities under sample-space ignorance (i.e., ignorance of what the possible outcomes are in a decision). The framework used for comparisons with human judgments is primarily due to Walley (1991, 1996). Five studies are reported which test four of Walley's prescriptions for judgment under sample-space ignorance, as well as assessing the impact of the number of observations and types of events on subjective lower and upper probability estimates. The paper concludes with a synopsis of future directions for empirical research on subjective imprecise probability judgments.","PeriodicalId":377089,"journal":{"name":"International Symposium on Imprecise Probabilities and Their Applications","volume":"146 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134401126","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An Experimental Study of Updating Ambiguous Beliefs","authors":"M. Cohen, I. Gilboa, J. Jaffray, D. Schmeidler","doi":"10.1017/S1357530900000132","DOIUrl":"https://doi.org/10.1017/S1357530900000132","url":null,"abstract":"‘Ambiguous beliefs’ are beliefs which are inconsistent with a unique, additive prior. The problem of their update in face of new information has been dealt with in the theoretical literature, and received several contradictory answers. In particular, the ‘maximum likelihood update’ and the ‘full Bayesian update’ have been axiomatized. This experimental study attempts to test the descriptive validity of these two theories by using the Ellsberg experiment framework.","PeriodicalId":377089,"journal":{"name":"International Symposium on Imprecise Probabilities and Their Applications","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133525767","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fuzzy, probabilistic and stochastic modelling of an elastically bedded beam","authors":"M. Oberguggenberger","doi":"10.1007/3-540-26847-2_10","DOIUrl":"https://doi.org/10.1007/3-540-26847-2_10","url":null,"abstract":"","PeriodicalId":377089,"journal":{"name":"International Symposium on Imprecise Probabilities and Their Applications","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116673047","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Graphical Models for Conditional Independence Structures","authors":"B. Vantaggi","doi":"10.1017/9781108604574.011","DOIUrl":"https://doi.org/10.1017/9781108604574.011","url":null,"abstract":"","PeriodicalId":377089,"journal":{"name":"International Symposium on Imprecise Probabilities and Their Applications","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127755455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Combining Belief Functions Issued from Dependent Sources","authors":"M. Cattaneo","doi":"10.3929/ETHZ-A-004531249","DOIUrl":"https://doi.org/10.3929/ETHZ-A-004531249","url":null,"abstract":"Dempster’s rule for combining two belief functions assumes the independence of the sources of information. If this assumption is questionable, I suggest to use the least specific combination minimizing the conflict among the ones allowed by a simple generalization of Dempster’s rule. This increases the monotonicity of the reasoning and helps us to manage situations of dependence. Some properties of this combination rule and its usefulness in a generalization of Bayes’ theorem are then considered.","PeriodicalId":377089,"journal":{"name":"International Symposium on Imprecise Probabilities and Their Applications","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114165198","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}