Posterior consistency of Dirichlet mixtures in density estimation. (English) Zbl 0932.62043

Summary: A Dirichlet mixture of normal densities is a useful choice for a prior distribution on densities in the problem of Bayesian density estimation. In the recent years, an efficient Markov chain Monte Carlo method for the computation of the posterior distribution has been developed. The method has been applied 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.


62G07 Density estimation
62G20 Asymptotic properties of nonparametric inference
62F15 Bayesian inference
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