Belief in Belief Functions: An Examination of Shafer's Canonical Examples

Abstract

In the canonical examples underlying Shafer-Dempster theory, beliefs over the hypotheses of interest are derived from a probability model for a set of auxiliary hypotheses. A belief function differs from a Bayesian probability model in that one does not condition on those parts of the evidence for which no probabilities are specified. The significance of this difference in conditioning assumptions is illustrated with two examples giving rise to identical belief functions but different Bayesian probability distributions.