Analysis of Multiple-try Metropolis via Poincar\'e inequalities
Computation
2025-11-18 v2 Probability
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.
Keywords
Cite
@article{arxiv.2504.18409,
title = {Analysis of Multiple-try Metropolis via Poincar\'e inequalities},
author = {Rocco Caprio and Sam Power and Andi Q. Wang},
journal= {arXiv preprint arXiv:2504.18409},
year = {2025}
}