Range of posterior measures for priors with arbitrary contaminations

Abstract

The robustness or sensitivity of some posterior criteria to specification of the prior distribution is considered. We model the uncertainties in an elicited prior, π0, by a ∊-contamination class , and consider the case where the class of contaminations Q = {all probability distributions}. The ranges of the posterior mean and the posterior variance, as the prior distribution varies over р, are determined. Examples involving normal and Poisson likelihoods are given.