A Bayes Procedure for Selecting the Population with the Largest pth Quantile.

The Bayesian approach has not been very fruitful in treating nonparametric statistical problems, due to the difficulty in finding mathematically tractable prior distributions on a set of probability measures. The theory of the Dirichlet process has been developed recently. The process generates randomly a family of probability distributions which can be taken as a family of prior distributions for the Bayesian analysis of some nonparametric statistical problems. This paper deals with the problem of selection a distribution with the largest pth quantile value, from k or 2 given distributions. It is assumed a priori that the given distributions have been generated from a Dirichlet process.