Selection of the Most Probable Best

In practice, simulation parameters are estimated from finite data, which introduces model uncertainty. In “Selection of the Most Probable Best,” Taeho Kim, Kyoung-Kuk Kim, and Eunhye Song propose a new estimator of the optimum, the most probable best (MPB), for ranking and selection (R&S) when the model uncertainty is characterized by a posterior distribution on the parameter given data. Defined as the solution with the largest posterior probability of optimality, selecting the MPB requires simulating at all parameter-solution combinations. The authors focus on when the posterior has a finite support and derive the convergence rate of the probability of correctly selecting the MPB as a function of sampling fractions of all solution-parameter pairs. They propose a lower bound on the rate function that allows easier characterization of the optimal sampling fractions and devise a sequential sampling algorithm from it. The algorithm shows superior empirical performance over benchmarks.