A Bayes procedure for selecting the population with the largest pth quantile (Q802244)

The Bayes method is seldom applied to nonparametric statistical problems, for the reason that it is hard to find mathematically tractable prior distributions on a set of probability measures. However, it is found that the Dirichlet process generates randomly a family of probability distributions which can be taken as a family of prior distributions for an application of the Bayes method to such problems. This paper presents a Bayesian analysis of a nonparametric problem of selecting a distribution with the largest pth quantile value, from \(k\geq 2\) given distributions. It is assumed a priori that the given distributions have been generated from a Dirichlet process.