Statistical Inference with Belief Functions and Possibility Measures: A Discussion of Basic Assumptions

This paper reconsiders the problem of statistical inference from the standpoint of evidence theory and possibility theory. The Generalized Bayes theorem due to Smets is described and illustrated on a small canonical example. Critiques addressed to this model are discussed as well as the robust Bayesian solution. Finally, the proposal made by Shafer to exploit likelihood information in terms of consonant belief function within the scope of possibility theory is reconsidered. A major objection to this approach, due to a lack of commutativity between combination and conditioning, is circumvented by assuming that the set of hypotheses or parameter values is rich enough.