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 2 given
distributions. It is assumed a priori that the given distributions have
been generated from a Dirichlet process.