Convergence rates and moments of Markov chains associated with the mean of Dirichlet processes

We give necessary and sufficient conditions for geometric and polynomial ergodicity of a Markov chain on the real line with invariant distribution equal to the distribution of the mean of a Dirichlet process with parameter [alpha]. This extends the applicability of a recent MCMC method for sampling from . We show that the existence of polynomial moments of [alpha] is necessary and sufficient for geometric ergodicity, while logarithmic moments of [alpha] are necessary and sufficient for polynomial ergodicity. As corollaries it is shown that [alpha] and have polynomial moments of the same order, while the order of the logarithmic moments differ by one.Dirichlet processes Markov chains Markov chain Monte Carlo Geometric and polynomial ergodicity Polynomial and logarithmic moments