Belief in Belief Functions: An Examination of Shafer's Canonical Examples
This work addresses foundational issues in uncertainty reasoning for researchers in AI and statistics, but it is incremental as it builds on existing canonical examples.
The paper examines the difference between belief functions and Bayesian probability models in Shafer-Dempster theory, showing that identical belief functions can correspond to different Bayesian distributions due to variations in conditioning assumptions.
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. Beliefs are derived via a compatibility relation connecting the auxiliary hypotheses to subsets of the primary 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.