Posterior consistency of Dirichlet mixtures in density estimation

A Dirichlet mixture of normal densities is a useful choice for a prior dist ribution on densities in the problem of Bayesian density estimation. In the recent years, efficient Markov chain Monte Carlo method for the computatio n of the posterior distribution has been developed. The method has been app lied to data arising from different fields of interest. The important issue of consistency was however left open. In this paper, we settle this issue in affirmative.