Prior Envelopes Based on Belief Functions

Abstract

We show that the mathematical structure of belief functions makes them suitable for generating classes of prior distributions to be used in robust {B}ayesian inference. In particular, the upper and lower bounds of the posterior probability content of a measurable subset of the parameter space may be calculated directly in terms of upper and lower expectations (Theorem 4.1). We also extend an integral representation given by Dempster to infinite sets (Theorem 2.1).