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Bayes’ theorem for Choquet capacities. (English) Zbl 0736.62026

Authors’ 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 \({\mathcal P}\). The bound is a rational function of two Choquet integrals. If \({\mathcal P}\) 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.

MSC:

62F15 Bayesian inference
62B99 Sufficiency and information
62F35 Robustness and adaptive procedures (parametric inference)
62A01 Foundations and philosophical topics in statistics
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