Issues in Bayesian Loss Robustness

Bayesian robustness has concentrated mainly on checking sensitivity of a Bayesian analysis with respect to changes in the prior or the model. We deal here with several issues concerning robust Bayesian analysis with respect to the loss function. Stemming from foundational results, we suggest that a main computational objective would be the obtainment of the set of nondominated alternatives. We then discuss a number of structural questions concerning the nondominated set, mainly its existence and relation with the set of Bayes alternatives. We then discuss procedures to compute or approximate the nondominated set in several important statistical problems. Since this set may be too big to reach a nal decision , we mention some problems concerning gathering additional information.