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Convergence Rates of Attractive-Repulsive MCMC Algorithms

Author

Listed:
  • 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)

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.

Suggested Citation

  • Yu Hang Jiang & Tong Liu & Zhiya Lou & Jeffrey S. Rosenthal & Shanshan Shangguan & Fei Wang & Zixuan Wu, 2022. "Convergence Rates of Attractive-Repulsive MCMC Algorithms," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 2029-2054, September.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:3:d:10.1007_s11009-021-09909-y
    DOI: 10.1007/s11009-021-09909-y
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    References listed on IDEAS

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    1. Matthews, Peter, 1993. "A slowly mixing Markov chain with implications for Gibbs sampling," Statistics & Probability Letters, Elsevier, vol. 17(3), pages 231-236, June.
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