A note on convergence rates of Gibbs sampling for nonparametric mixtures.

We present a mathematical analysis of a class of Gibbs sampler algorithms for nonparametric mixtures, which use Dirichlet process priors and have updating steps which are partially discrete and partially continuous. We prove that such Gibbs samplers are uniformly ergodic, and we give a quantitative bound on their convergence rate. In a special case we can give a much sharper quantitative bound; however, in general the problem of sharper quantitative bounds remains open.

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