Ricerc@Sapienza

In Bayesian inference, the two most widely used methods for set estimation of an unknown one-dimensional parameter are equal-tails and highest posterior density intervals. The resulting estimates may be quite different for specific observed samples but, at least for standard but relevant models, they tend to become closer and closer as the sample size increases. In this article we propose a pre-posterior method for measuring the progressive alignment between these two classes of intervals and discuss relationships with the skewness of the posterior distribution.

In Bayesian analysis of clinical trials data, credible intervals are widely used for inference on unknown parameters of interest, such as treatment effects or differences in treatments effects. Highest Posterior Density (HPD) sets are often used because they guarantee the shortest length. In most of standard problems, closed-form expressions for exact HPD intervals do not exist, but they are available for intervals based on the normal approximation of the posterior distribution.