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arXiv · 2504.18409

Analysis of Multiple-try Metropolis via Poincar\'e inequalities

Rocco Caprio·Sam Power·Andi Q. Wang
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Abstract

We study the Multiple-try Metropolis algorithm using the framework of Poincar\'e inequalities. We describe the Multiple-try Metropolis as an auxiliary variable implementation of a resampling approximation to an ideal Metropolis--Hastings algorithm. Under suitable moment conditions on the importance weights, we derive explicit Poincar\'e comparison results between the Multiple-try algorithm and the ideal algorithm. We characterize the spectral gap of the latter, and finally in the Gaussian case prove explicit non-asymptotic convergence bounds for Multiple-try Metropolis by comparison.

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Rocco Caprio, Sam Power, Andi Q. Wang. 2025-04-25. Analysis of Multiple-try Metropolis via Poincar\'e inequalities. https://arxiv.org/abs/2504.18409

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