## Bayes' Theorem for Choquet Capacities

journal contribution

posted on 01.09.1990, 00:00 by Larry A. Wasserman, Joseph B. KadaneWe 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.