A likelihood-informed approach for myopically minimizing Bayesian posterior risk

Ranking and selection uses stochastic simulation to identify the optimal design from alternatives. This work aims to minimize the probability of incorrect selection by allocating a limited simulation budget among the designs. With the true optimal design unknown, this objective function lacks closed form. Under the expected value of information framework, existing methods approximate the objective using the conditional probability that the design with the best sample mean is optimal. This allows comparison of the potential information gain from different allocation decisions. In contrast to using this conditional probability, we propose a likelihood-informed procedure that incorporates the probability of each design being optimal when comparing the potential information gains. Using a two-design example, results show our procedure generates a better approximation of the objective compared to existing methods. Our proposed approach also demonstrates superior performance in minimizing the probability of incorrect selection for both neutral and flat mean instances.