On bayesian robustness: an asymptotic approach

Abstract

This paper presents a new asymptotic approach to study the robustness of Bayesian inference to changes on the prior distribution. We study the robustness of the posterior density score function when the uncertainty about the prior distribution has been restated as a problem of uncertainty about the model parametrization. Classical robustness tools, such as the influence function and the maximum bias function, are defined for uniparametric models and calculated for the location case. Possible extensions to other models are also briefly discussed.