Bayesian Credible Set Optimality
From Jane Harvill
The goal of obtaining a smallest confidence set with a specified coverage probability can also be attained using Bayesian criteria. If we have a posterior distribution π(θ|x), we want to find the set C(x) with coverage probability 1 − α that has a property known as highest posterior density (HPD). This property is defined, and obtaining a Bayesian credible set with HPD is illustrated.