On rates of convergence for posterior distributions in infinite–dimensional models.

Abstract

This paper introduces a new approach to the study of rates of convergence for posterior distributions. It is a natural extension of a recent approach to the study of Bayesian consistency. Crucially, no sieve or entropy measures are required and so rates do not depend on the rate of convergence of the corresponding sieve maximum likelihood estimator. In particular, we improve on current rates for mixture models.Hellinger consistency; mixture of Dirichlet process; posterior distribution; rates of convergence