Convergence Rates of Attractive-Repulsive MCMC Algorithms

2020/12/08 by Jiang, Yu Hang, Liu, Tong, Lou, Zhiya +4 · 1 citation
#60J10(primary) #60J20 #60J22(secondary) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2012.04786

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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