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arXiv · 2012.04786

Convergence Rates of Attractive-Repulsive MCMC Algorithms

Yu Hang Jiang·Tong Liu·Zhiya Lou·Jeffrey S. Rosenthal·Shanshan Shangguan·Fei Wang·Zixuan Wu
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Abstract

We consider MCMC algorithms for certain particle systems which include both attractive and repulsive forces, making their convergence analysis challenging. We prove that a version of these algorithms on a bounded state space is uniformly ergodic with an explicit quantitative convergence rate. We also prove that a version on an unbounded state-space is still geometrically ergodic, and then use the method of shift-coupling to obtain an explicit quantitative bound on its convergence rate.

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Yu Hang Jiang, Tong Liu, Zhiya Lou, Jeffrey S. Rosenthal, Shanshan Shangguan, Fei Wang, Zixuan Wu. 2020-12-08. Convergence Rates of Attractive-Repulsive MCMC Algorithms. https://arxiv.org/abs/2012.04786

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