Convergence Rates of Attractive-Repulsive MCMC Algorithms

Yu Hang Jiang, Tong Liu, Zhiya Lou, Jeffrey S. Rosenthal (), Shanshan Shangguan, Fei Wang and Zixuan Wu
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Yu Hang Jiang: University of Toronto
Tong Liu: University of Toronto
Zhiya Lou: University of Toronto
Jeffrey S. Rosenthal: University of Toronto
Shanshan Shangguan: University of Toronto
Fei Wang: University of Toronto
Zixuan Wu: University of Toronto

Methodology and Computing in Applied Probability, 2022, vol. 24, issue 3, 2029-2054

Abstract: 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 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.

Keywords: Markov chain Monte Carlo; Convergence rate; Particle system; Shift coupling (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11009-021-09909-y

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