Date of Original Version
Abstract or Description
We give an upper bound for the posterior probability of a measurable set A when the prior lies in a class of probability measures P. The bound is a rational function of two Choquet integrals. If P is weakly compact and is closed with respect to majorization, then the bound is sharp if and only if the upper prior probability is 2-alternating. The result is used to compute -bounds for several sets of priors used in robust Bayesian inference. The result may be regarded as a characterization of 2-alternating Choquet capacities.
The Annals of Statistics, 18, 3, 1328-1339.