Posterior probability of correct selection

Abstract

The selection of the “best” of a number of treatments is studied from a Bayesian point of view using normal likelihoods and priors. The posterior probability of correct selection is expressed as a function of the prior variance and is estimated using a parametric empirical Bayes' approach. A compromise between this method and the heirarchical Bayes' approach is investigated. Subset selection is considered from similar points of view. The analysis of a numerical example reveals a problem for which a solution is suggested.

Keywords:

• Selection
• Bayesian
• empirical Bayes'
• heirarchical Bayes'
• subset selection