A note on the progressive overlap of two alternative Bayesian intervals

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. We illustrate the implementation of the method using the software R for the Poisson model and for some standard examples.