  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.
