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August 2022 An adaptive multiple-try Metropolis algorithm
Simon Fontaine, Mylène Bédard
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Bernoulli 28(3): 1986-2011 (August 2022). DOI: 10.3150/21-BEJ1408

Abstract

Markov chain Monte Carlo (MCMC) methods, specifically samplers based on random walks, often have difficulty handling target distributions with complex geometry such as multi-modality. We propose an adaptive multiple-try Metropolis algorithm designed to tackle such problems by combining the flexibility of multiple-proposal samplers with the user-friendliness and optimality of adaptive algorithms. We prove the ergodicity of the resulting Markov chain with respect to the target distribution using common techniques in the adaptive MCMC literature. In a Bayesian model for loss of heterozygosity in cancer cells, we find that our method outperforms traditional adaptive samplers, non-adaptive multiple-try Metropolis samplers, and various more sophisticated competing methods.

Acknowledgements

This work has been supported by the Natural Sciences and Engineering Research Council of Canada.

Citation

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Simon Fontaine. Mylène Bédard. "An adaptive multiple-try Metropolis algorithm." Bernoulli 28 (3) 1986 - 2011, August 2022. https://doi.org/10.3150/21-BEJ1408

Information

Received: 1 December 2020; Published: August 2022
First available in Project Euclid: 25 April 2022

Digital Object Identifier: 10.3150/21-BEJ1408

Keywords: Adaptive scaling , ergodicity , limit theorem , loss of heterozygosity , multiple candidates , random walk sampler , robust adaptation

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Vol.28 • No. 3 • August 2022
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