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

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  • Jarner, S. F.
  • Tweedie, R. L.

Abstract

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.

Suggested Citation

  • Jarner, S. F. & Tweedie, R. L., 2002. "Convergence rates and moments of Markov chains associated with the mean of Dirichlet processes," Stochastic Processes and their Applications, Elsevier, vol. 101(2), pages 257-271, October.
    • Handle: RePEc:eee:spapps:v:101:y:2002:i:2:p:257-271
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    References listed on IDEAS

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    1. Roberts, G. O. & Tweedie, R. L., 1999. "Bounds on regeneration times and convergence rates for Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 80(2), pages 211-229, April.
    2. P. Muliere & P. Secchi, 1996. "Bayesian nonparametric predictive inference and bootstrap techniques," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(4), pages 663-673, December.
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