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Convergence Rates of Attractive-Repulsive MCMC Algorithms

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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 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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Acknowledgements

We thank the editor and referee for very helpful suggestions which have led to many improvements of this paper.

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Authors and Affiliations

  1. Department of Statistical Sciences, University of Toronto, 700 University Avenue, 9th Floor, Toronto, M5G 1X6, Ontario, Canada

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

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  1. Yu Hang Jiang
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  2. Tong Liu
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  3. Zhiya Lou
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  4. Jeffrey S. Rosenthal
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  5. Shanshan Shangguan
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  6. Fei Wang
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  7. Zixuan Wu
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Correspondence to Jeffrey S. Rosenthal.

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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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