Robust Bayesian credible sets
by
Sudip Bose
The George Washington University

We propose a robust Bayesian approach to selecting a credible set. Suppose that uncertainty about the prior probability distribution is modeled by using a class G of priors in a `neighborhood’ of a starting prior p₀. Among the class of sets with credibility g under p₀, we choose the one that maximizes the minimum posterior probability of including the parameter as the prior varies over G. This procedure is also G-minimax in a decision theoretic sense. We find the optimally robust credible set for three neighborhood classes G: the epsilon-contamination class, the density ratio class, and the density bounded class. The maximum likelihood credible set is seen to have appealing optimality properties.

Date received: March 30, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caxa-30.