Anomalies arising from a Bayesian analysis of Dempster's upper and lower probabilities

Abstract

Dempster (1967) calculates upper and lower probabilities for samples from a finite univariate population. These are to be used to make inferences about a second sample to be drawn from the same population. Here we show, by example, that these inferences are not compatible with a Bayesian analysis of the problem. Specifically, Example 1 shows that the upper and lower probabilities are not bounds for Bayesian posterior probabilities derived, from ‘no prior information’, and Example 2 shows that in some sense Dempster's method does not permit any nondegenerate prior distribution.