Posterior consistency of Dirichlet mixtures in density estimation

Open Access

1 March 1999

journal article
Published by Institute of Mathematical Statistics in The Annals of Statistics

Vol. 27 (1) , 143-158
https://doi.org/10.1214/aos/1018031105

Abstract

A Dirichlet mixture of normal densities is a useful choice for a prior distribution on densities in the problem of Bayesian density estimation. In recent years, 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.

Keywords

This publication has 10 references indexed in Scilit:

Information-theoretic determination of minimax rates of convergence
The Annals of Statistics, 1999
Practical Bayesian density estimation using mixtures of normals
Journal of the American Statistical Association, 1997
Weak Convergence
Published by Springer Nature ,1996
Uniformly Powerful Goodness of Fit Tests
The Annals of Statistics, 1989
On a Class of Bayesian Nonparametric Estimates: I. Density Estimates
The Annals of Statistics, 1984
BAYESIAN DENSITY ESTIMATION BY MIXTURES OF NORMAL DISTRIBUTIONS11This research was partially supported by the National Science Foundation under Grant MCS77-2121.
Published by Elsevier ,1983
The Tails of Probabilities Chosen From A Dirichlet Prior
The Annals of Statistics, 1982
Bayes Risk Consistency of Nonparametric Bayes Density Estimates2
Australian Journal of Statistics, 1982
Convergence of Estimates Under Dimensionality Restrictions
The Annals of Statistics, 1973
On Bayes procedures
Probability Theory and Related Fields, 1965