Importance is Important: Generalized Markov Chain Importance Sampling Methods

Guanxun Li; Aaron Smith; Quan Zhou

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arXiv · 2304.06251

Importance is Important: Generalized Markov Chain Importance Sampling Methods

Guanxun Li·Aaron Smith·Quan Zhou

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Abstract

We show that for any multiple-try Metropolis algorithm, one can always accept the proposal and evaluate the importance weight that is needed to correct for the bias without extra computational cost. This results in a general, convenient, and rejection-free Markov chain Monte Carlo (MCMC) sampling scheme. By further leveraging the importance sampling perspective on Metropolis--Hastings algorithms, we propose an alternative MCMC sampler on discrete spaces that is also outside the Metropolis--Hastings framework, along with a general theory on its complexity. Numerical examples suggest that the proposed algorithms are consistently more efficient than the original Metropolis--Hastings versions.

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Guanxun Li, Aaron Smith, Quan Zhou. 2023-04-13. Importance is Important: Generalized Markov Chain Importance Sampling Methods. https://arxiv.org/abs/2304.06251

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