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August 2001 Markov chain Monte Carlo estimation of the law of the mean of a Dirichlet process
Alessandra Guglielmi, Richard L. Tweedie
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Bernoulli 7(4): 573-592 (August 2001).

Abstract

The distribution $\mathcal{M}_\alpha$ of the mean $\Gamma_\alpha$ of a Dirichlet process on the real line, with parameter $\alpha$, can be characterized as the invariant distribution of a real Markov chain $\Gamma_n$. In this paper we prove that, if $\alpha$ has finite expectation, the rate of convergence (in total variation) 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 α has a support which is not doubly infinite. We use this to study an approximation procedure for $\mathcal{M}_\alpha$, and evaluate the approximation error in simulating $\mathcal{M}_\alpha$ using this chain. We include examples for a comparison with some of the existing procedures for approximating $\mathcal{M}_\alpha$, and show that the Markov chain approximation compares well with other methods.

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Alessandra Guglielmi. Richard L. Tweedie. "Markov chain Monte Carlo estimation of the law of the mean of a Dirichlet process." Bernoulli 7 (4) 573 - 592, August 2001.

Information

Published: August 2001
First available in Project Euclid: 17 March 2004

zbMATH: 1005.62073
MathSciNet: MR2002J:62107

Keywords: Dirichlet process , Markov chain Monte Carlo , Markov chains with general state space , mean functional , rate of convergence

Rights: Copyright © 2001 Bernoulli Society for Mathematical Statistics and Probability

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Vol.7 • No. 4 • August 2001
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