Rates of convergence of the Hastings and Metropolis algorithms

Mengersen, Kerrie L. & Tweedie, Richard L. (1996) Rates of convergence of the Hastings and Metropolis algorithms. The Annals of Statistics, 24(1), pp. 101-121.

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We apply recent results in Markov chain theory to Hastings and Metropolis algorithms with either independent or symmetric candidate distributions, and provide necessary and sufficient conditions for the algorithms to converge at a geometric rate to a prescribed distribution $pi$. In the independence case (in $mathbb{R}^k$) these indicate that geometric convergence essentially occurs if and only if the candidate density is bounded below by a multiple of $pi$; in the symmetric case (in $mathbb{R}$ only) we show geometric convergence essentially occurs if and only if $pi$ has geometric tails. We also evaluate recently developed computable bounds on the rates of convergence in this context: examples show that these theoretical bounds can be inherently extremely conservative, although when the chain is stochastically monotone the bounds may well be effective.

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ID Code: 13133
Item Type: Journal Article
Refereed: Yes
Additional Information: The contents of this journal can be freely accessed online via the journal's web page (see hypertext link).
Additional URLs:
DOI: 10.1214/aos/1033066201
ISSN: 0090-5364
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Copyright Owner: Copyright 1996 Institute of Mathematical Statistics
Copyright Statement: Reproduced in accordance with the copyright policy of the publisher.
Deposited On: 25 Mar 2008 00:00
Last Modified: 09 Jun 2010 12:57

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