Adaptive Convergence Rates of a Dirichlet Process Mixture of Multivariate Normals
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Duke University
February 6, 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
