Bayesian robustness under likelihood and prior distortion

Abstract

The choice of sampling models and, in the Bayesian framework, of prior distributions is a critical aspect in any statistical analysis. Sometimes small changes in their specification could have a significant impact on inferences and decisions. Therefore, the study of the robustness (or sensitivity) of the inferences with respect to those changes is a relevant, non-trivial task. We are, in particular, interested in Bayesian robustness when either the (univariate or multivariate) prior or the likelihood function are perturbed through distortion functions. For the prior robustness we consider classes of distributions defined considering stochastic order and their consequences on the estimation of the quantities of interest, while for the likelihood robustness we consider infinitesimal changes. The two approaches are representative of global and local robustness, respectively.