QUT ePrints

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.

View at publisher

Abstract

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.

Impact and interest:

162 citations in Scopus
Search Google Scholar™
151 citations in Web of Science®

Citation countsare sourced monthly from Scopus and Web of Science® citation databases.

These databases contain citations from different subsets of available publications and different time periods and thus the citation count from each is usually different. Some works are not in either database and no count is displayed. Scopus includes citations from articles published in 1996 onwards, and Web of Science® generally from 1980 onwards.

Citations counts from the Google Scholar™ indexing service can be viewed at the linked Google Scholar™ search.

Full-text downloads:

228 since deposited on 25 Mar 2008
64 in the past twelve months

Full-text downloadsdisplays the total number of times this work’s files (e.g., a PDF) have been downloaded from QUT ePrints as well as the number of downloads in the previous 365 days. The count includes downloads for all files if a work has more than one.

ID Code: 13133
Item Type: Journal Article
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
Last Modified: 09 Jun 2010 22:57

Export: EndNote | Dublin Core | BibTeX

Repository Staff Only: item control page