Adaptive Convergence Rates of a Dirichlet Process Mixture of Multivariate Normals

Details Adaptive Convergence Rates of a Dirichlet Process Mixture of Multivariate Normals Adaptive Convergence Rates of a Dirichlet Process Mixture of Multivariate Normals

2011-11-17

arxiv.org/abs/1111.4148v1

Mathematics

Statistics Theory

12 pages

Scientific paper

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.

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