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

TL;DR

This paper examines the foundational examples of Shafer's belief functions, highlighting how belief functions differ from Bayesian probabilities in their conditioning assumptions through illustrative examples.

Contribution

It clarifies the conceptual differences between belief functions and Bayesian probabilities using canonical examples, emphasizing the significance of conditioning assumptions.

Findings

Belief functions do not condition on unspecified evidence parts.

Canonical examples can produce identical belief functions but different Bayesian distributions.

The difference in conditioning impacts interpretation of evidence.

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. 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.