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August 2022 Exact convergence analysis of the independent Metropolis-Hastings algorithms
Guanyang Wang
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Bernoulli 28(3): 2012-2033 (August 2022). DOI: 10.3150/21-BEJ1409

Abstract

A well-known difficult problem regarding Metropolis-Hastings algorithms is to get sharp bounds on their convergence rates. Moreover, a fundamental but often overlooked problem in Markov chain theory is to study the convergence rates for different initializations. In this paper, we study the two issues mentioned above of the Independent Metropolis-Hastings (IMH) algorithms on both general and discrete state spaces. We derive the exact convergence rate and prove that the IMH algorithm’s different deterministic initializations have the same convergence rate. We get the exact convergence speed for IMH algorithms on general state spaces.

Acknowledgement

The author would like to thank Richard Smith and Persi Diaconis for helpful discussions, and Jeffrey Rosenthal for pointing out some useful references, and David Sichen Wu and Zhengqing Zhou for helpful suggestions in improving this paper. The author would like to thank the Editor, the Associate Editor, and two referees for many very helpful suggestions.

Citation

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Guanyang Wang. "Exact convergence analysis of the independent Metropolis-Hastings algorithms." Bernoulli 28 (3) 2012 - 2033, August 2022. https://doi.org/10.3150/21-BEJ1409

Information

Received: 1 January 2021; Published: August 2022
First available in Project Euclid: 25 April 2022

Digital Object Identifier: 10.3150/21-BEJ1409

Keywords: exact convergence rate , Independent Metropolis-Hastings , Markov chain Monte Carlo

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Vol.28 • No. 3 • August 2022
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