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

Ksenia Kasianova; Mark Kelbert

Vol. 28 No. 2 (2023)

Regular Articles

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

Published 2023-10-19

Ksenia Kasianova
Mark Kelbert

Ksenia Kasianova
National Research University Higher School of Economics

Mark Kelbert
National Research University Higher School of Economics

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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.

Keywords

Differential entropy, Gaussian limiting theorem, Kullback-Leibler divergence, Selberg's integral, Multivariate Selberg Beta distribution, Expert elicitation

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