Dynamic Sampling Allocation and Design Selection
提出一个动态框架，同时处理顺序采样分配和最优设计选择，引入集成正确选择概率来优化策略，并设计近似方法提高小样本下的性能。
We formulate the statistical selection problem in a general dynamic framework comprising fully sequential sampling allocation and optimal design selection. Because the traditional probability of correct selection measure is not sufficient to capture both aspects in this more general framework, we introduce the integrated probability of correct selection to better characterize the objective. As a result, the usual selection policy of choosing the design with the largest sample mean as the estimate of the best is no longer necessarily 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 the posterior mean and the correlation structure induced by the posterior variance. Because determining the optimal selection policy is generally intractable, we also devise an approximation scheme to efficiently approximate the optimal selection policy. For the allocation policy, we study an asymptotic policy called general Bayesian budget allocation, which is comprised of a sampling statistic and a sequential rule. The optimal computing budget allocation algorithm can be interpreted as a special case of the asymptotical sampling statistics. Numerical examples are provided to illustrate the potential performance improvements, especially in small sample behavior.