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# Bayes' Theorem for Choquet Capacities

journal contribution
posted on 01.09.1990, 00:00 by Larry A. Wasserman, Joseph B. Kadane
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.

01/09/1990

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