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.

The two most commonly used methods for Bayesian set estimation of an unknown one-dimensional parameter are equal-tails and highest posterior density intervals. The resulting estimates may be numerically different for specific observed samples but they tend to become closer and closer as the sample size increases. In this article we consider a pre-posterior measure of the progressive overlap between these two types of intervals and relationships with the skewness of the posterior distribution.