A Bayesian Approach to a Nonparametric Problem of Selecting the Population With the Largest p-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 distributions on a given sample space. The theory of Dirichlet process has been developed recently. The process generates prior distributions on spaces of probability measures. The prior distributions can be used in Bayesian analysis of nonparametric statistical problems. This paper presents a Bayesian analysis of the problem of selecting a distribution with the largest p-quantile value from K = or > 2 given distributions, using prior prior distributions generated from a Dirichlet process. The probability of a correct selection is derived for a selection procedure for the given problem.