Une formulation simplifiée du théorème de Bayes généralisé

International audienceIn this paper we present a simple formulation of the Generalized Bayes' Theorem (GBT) which extends Bayes' theorem in the framework of belief functions. We also present the condition under which this new formulation is valid. We illustrate our theoretical results with simple examples

Total belief theorem and conditional belief functions

In this paper new theoretical results for reasoning with belief functions are obtained and discussed. After a judicious decomposition of the set of focal elements of a belief function, we establish the Total Belief Theorem (TBT) which is the direct generalization of the Total Probability Theorem when working in the framework of belief functions. The TBT is also generalized for dealing with different frames of discernments thanks to Cartesian product space. From TBT, we can derive and define formally the expressions of conditional belief functions which are consistent with the bounds of imprecise conditional probability. This work provides a direct establishment and solid justification of Fagin-Halpern belief conditioning formulas. The well-known Bayes' Theorem of Probability Theory is then generalized in the framework of belief functions and we illustrate it with an example at the end of this paper

A Generalization of Bayesian Inference in the Dempster-Shafer Belief Theoretic Framework

In the literature, two main views of Dempster-Shafer (DS) theory are espoused: DS theory as evidence (as described in Shafer's seminal book) and DS theory as a generalization of probability. These two views are not always consistent. In this paper, we employ the generalized probability view of DS theory to arrive at results that allow one to perform Bayesian inference within the DS theoretic (DST) framework. The importance of this generalization is its capability of handling a wider variety of data imperfections, a feature inherited from the DST framework. In the process of developing these results akin to Bayesian inference, we also arrive at an evidence combination strategy which is consistent with the generalized probability view of DS theory, a feature lacking in the popular Dempster's combination rule (DCR). Finally, using the data from a political science survey, we demonstrate the application of our results on an experiment which attempts to gauge the hidden attitude of an individual from his/her observed behavior