Markov chain Monte Carlo estimation of the law of the mean of a Dirichlet process

The distribution. N-alpha of the mean Gamma (alpha) of a Dirichlet process on the real line, with parameter a, can be characterized as the invariant d istribution of a real Markov chain Gamma (n), In this paper we prove that, if alpha has finite expectation, the rate of convergence (in total variatio n) of Gamma (n) to Gamma (alpha) is geometric. Upper bounds on the rate of convergence are found which seem effective, especially in the case where a has a support which is not doubly infinite. We use this to study an approxi mation procedure for. N-alpha, and evaluate the approximation error in simu lating. N-alpha using this chain. We include examples for a comparison with some of the existing procedures for approximating, N-alpha, and show that the Markov chain approximation compares well with other methods.