A simple diagnostic tool for local prior sensitivity

This paper presents a simple diagnostic tool to assess the sensitivity of the posterior mode in the presence of an infinitesimal contamination in the prior distribution. The proposed diagnostic measure is easy to compute and can be used as a first step in judging the robustness of the Bayesian inference. The procedure is illustrated in the estimation of the mean of a normal distribution. Some extensions of this diagnostic measure to the multivariate case and credibility intervals are briefly discussed.