Bayesian robustness under a skew-normal class of prior distribution

•A global sensitivity analysis with respect to a prior distributions is considered.•Skew-normal class of prior for the location parameter of a normal model is explored.•We obtained results of a Bayesian conjugation.•Closed-form expressions for posterior inferences are also obtained.•We discuss in what situations the robustness is achieved through a simulation study.

We develop a global sensitivity analysis to measure the robustness of the Bayesian estimators with respect to a class of prior distributions. This class arises when we consider multiplicative contamination of a base prior distribution. A similar structure was presented by van der Linde [12]. Some particular specifications for this multiplicative contamination class coincide with well known families of skewed distributions. In this paper, we explore the skew-normal multiplicative contamination class for the prior distribution of the location parameter of a normal model. Results of a Bayesian conjugation and expressions for some measures of distance between posterior means and posterior variance are obtained. We also elaborate on the behavior of the posterior means and of the posterior variances through a simulation study.