Adaptive Convergence Rates of a Dirichlet Process Mixture of Multivariate Normals

Abstract

It is shown that a simple Dirichlet process mixture of multivariate normals offers Bayesian density estimation with adaptive posterior convergence rates. Toward this, a novel sieve for non-parametric mixture densities is explored, and its rate adaptability to various smoothness classes of densities in arbitrary dimension is demonstrated. This sieve construction is expected to offer a substantial technical advancement in studying Bayesian non-parametric mixture models based on stick-breaking priors.

12 pages

References in corpus (2)

• Adaptive Bayesian estimation using a Gaussian random field with inverse Gamma bandwidth
• Adaptive Bayesian multivariate density estimation with Dirichlet mixtures

Cited by in corpus (1)

• Bayesian learning of joint distributions of objects