Gaussian limit theorem for posterior distribution in the problem on conflicting experts’ opinions

Abstract

Suppose we have $n$ experts who have their prior opinion about the unknown probability $q$  in the experiment with a binary outcome. It is known that experts' opinions are in conflict with each other. To model "conflicting" experts' opinions  a prior distribution based on Selberg's integral is constructed. We prove a theorem regarding the limiting properties of the posterior distribution. Also, differential entropy and Kullback-Leibler (KL) divergence of such posterior are studied.