Moment-Matching-Based Conjugacy Approximation for Bayesian Ranking and Selection

Abstract

We study the conjugacy approximation models in the context of Bayesian ranking and selection with unknown correlations. Under the assumption of normal-inverse-Wishart prior distribution, the posterior distribution remains a normal-inverse-Wishart distribution thanks to the conjugacy property when all alternatives are sampled at each step. However, this conjugacy property no longer holds if only one alternative is sampled at a time, an appropriate setting when there is a limited budget on the number of samples. We propose two new conjugacy approximation models based on the idea of moment matching. Both of them yield closed-form Bayesian prior updating formulas. We apply these updating formulas in Bayesian ranking and selection using the knowledge gradient method and show the superiority of the proposed conjugacy approximation models in applications of wind farm placement and computer model calibration.