Optimal credible intervals under alternative loss functions

This article deals with Bayesian interval estimation of the parameter of a statistical model from a decision-theoretic perspective. We consider the class of monotone loss functions, that take into account both size and posterior probability of the sets and that, under general conditions, guarantees the optimality of high- est posterior probability sets. More specifically, we focus on three families of loss functions: linear, rational and exponential. Resorting to numerical examples and simulations, we examine both posterior and pre-posterior features of these choices for the Poisson-Gamma model.