(Received February 21, 1991; revised February 27, 1992)
Abstract. Range of the posterior probability of an interval over the epsilon-contamination class Gamma = {pi = (1-epsilon)pi0 + epsilon q: q \in Q} is derived. Here, pi0 is the elicited prior which is assumed unimodal, epsilon is the amount of uncertainty in pi0, and Q is the set of all probability densities q for which pi = (1-epsilon)pi0 + epsilon q is unimodal with the same mode as that of pi0. We show that the sup (resp. inf) of the posterior probability of an interval is attained by a prior which is equal to (1-epsilon)pi0 except in one interval (resp. two disjoint intervals) where it is constant.
Key words and phrases: Posterior probability, unimodality preserving contaminations, Bayesian robustness.