Robust Bayesian Analysis with ϵ-Contaminations Partially Known

Abstract

SUMMARY Prior distributions of the form π=(1−ϵ)π0+ϵq,π0 being the base elicited prior, q being contamination and ϵ reflecting the amount of error in π0 that is deemed possible, are considered. It is assumed that π0 is completely specified and that only some quantiles of q are known. As π varies over this class, the ranges of the posterior mean and of the posterior probabilities of an arbitrary set are determined. Some examples including hypotheses testing related to a bivariate normal likelihood are given.