A dynamic framework for statistical selection problems

For the statistical selection problem we formulate a general framework comprising both sequential sampling allocation and optimal design selection, for which the traditional probability of correct selection measure is inadequate. Therefore, we introduce the integrated probability of correct selection to better characterize the objective. In this framework, the usual selection policy of choosing the design with the largest sample mean as the estimate of the best is no longer optimal. Rather, the optimal selection policy is to choose the design that maximizes the posterior integrated probability of correct selection, which is a function of both the posterior mean and the correlation structure induced by the posterior variance.