The Bayes method is seldom applied to nonparametric statisticalproblems, for the reason that it is hard to find mathematically tractableprior distributions on a set of probability measures. However, itis found that the Dirichlet process generates randomly a family of probabilitydistributions which can be taken as a family of prior distributionsfor an application of the Bayes method to such problems. Thispaper presents a Bayesian analysis of a nonparametric problem of selectinga distribution with the largest pth quantile value, from k 2 givendistributions. It is assumed a priori that the given distributions havebeen generated from a Dirichlet process.