Credible intervals

In this article we discuss set estimation in a Bayesian framework. In particular, we give a formal definition for a credible set in the general multivariate parameter setting and we will detail the unidimensional case when the set estimator is restricted to be an interval. Moreover, we comment upon differences and similarities between interval estimates via Bayesian and non-Bayesian methods. It is customary to ask that the credible set satisfies a minimum size optimality criterion, leading to the definition of highest posterior density regions. We mention some theoretical and computational issues of these optimal regions.