Statistical inference using belief functions: a reappraisal of General Bayes Theorem
Résumé
The General Bayes Theorem (GBT) as a generalization of Bayes theorem to the belief function framework. In probability theory, Bayes rule is used for three purposes: prediction based on observations, fusion of information, and learning (what statisticians call inference). The GBT supposedly addresses the latter task. It provides a method for deriving a belief function on a model parameter based on observations, when likelihoods are expressed as belief functions, without assuming any prior knowledge of the parameter. The GBT has been applied to diagnosis and classification tasks, but its use in statistical inference has remained very limited. After recalling the derivation of the GBT from first principles and some fundamental results, we try to analyze the potentials and the limitations of this approach to statistical inference. Its application to a very simple problem is discussed and compared to other approaches. A possibilistic counterpart of the GBT is also outlined.