Selecting the Best Among Good Populations Based on a Two-Stage Procedure: A Bayesian Approach with Applications

摘要

Several procedures have been studied to select the best among a set of new treatments (populations) which are better than a standard (or control) using two-stage procedures for the case of normal populations. One such procedure is to select the best based on the confidence intervals with a specified fixed width 2d after eliminating those populations which are worse than the standard based on the expected posterior losses. Several papers deal with this kind of problem but none of them is based on the so-called 100(1-2 alpha)% Highest Posterior Density (HPD) credible regions, which are conceptually equivalent to the confidence intervals, with a fixed width 2d. After retaining good populations based on the expected posterior losses, we set up a stopping rule Ni for constructing the HPD credible region for each selected population, which is asymptotically efficient and consistent. (Author)