Bayes' Theorem for Choquet Capacities
Larry A. Wasserman, Joseph B. Kadane
The Annals of Statistics · 1990 · Volume 18 · Issue 3
Abstract
We give an upper bound for the posterior probability of a measurable set $A$ when the prior lies in a class of probability measures $\mathscr{P}$. The bound is a rational function of two Choquet integrals. If $\mathscr{P}$ 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.
Keywords
2-alternating Choquet capacities, 62F15, 62F35, posterior bounds, robust Bayesian inference
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