Adaptive Convergence Rates of a Dirichlet Process Mixture of Multivariate Normals
Feb 5 2012
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.
Keywords:Bayesian multivariate density estimation, Non-parametric mixture, Posterior convergence, Sieve construction, Smoothness adaptation, Stick-breaking processes