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.
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04 November 2021
The 6th author name and abstract text was updated.
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We thank the editor and referee for very helpful suggestions which have led to many improvements of this paper.
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Jiang, Y.H., Liu, T., Lou, Z. et al. Convergence Rates of Attractive-Repulsive MCMC Algorithms. Methodol Comput Appl Probab 24, 2029–2054 (2022). https://doi.org/10.1007/s11009-021-09909-y
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DOI: https://doi.org/10.1007/s11009-021-09909-y