Implementation of a Robust Bayesian Method

Abstract

In this work we study robustness in Bayesian models through a generalization of the Normal distribution. We show new appropriate techniques in order to deal with this distribution in Bayesian inference. Then we propose two approaches to decide, in some applications, if we should replace the usual Normal model by this generalization. First, we pose this dilemma as a model rejection problem, using diagnostic measures. In the second approach we evaluate model’s predictive efficiency. We illustrate those perspectives with a simulation study, a non linear model and a longitudinal data model.