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Reducing rejection exponentially improves Markov chain Monte Carlo sampling

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  • Suwa, Hidemaro

Abstract

The choice of transition kernel critically influences the performance of the Markov chain Monte Carlo method. Despite the importance of kernel choice, guiding principles for optimal kernels have not been established. Here, we propose a one-parameter rejection control transition kernel that can be applied to various Monte Carlo samplings and demonstrate that the rejection process plays a major role in determining the sampling efficiency. Varying the rejection probability, we examine the autocorrelation time of the order parameter in the two- and three-dimensional ferromagnetic Potts models. Our results reveal that reducing the rejection rate leads to an exponential decrease in autocorrelation time in sequential spin updates and an algebraic reduction in random spin updates. The autocorrelation times of conventional algorithms almost fall on a single curve as a function of the rejection rate. The present transition kernel with an optimal parameter provides one of the most efficient samplers for general cases of discrete variables.

Suggested Citation

  • Suwa, Hidemaro, 2024. "Reducing rejection exponentially improves Markov chain Monte Carlo sampling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(C).
    • Handle: RePEc:eee:phsmap:v:633:y:2024:i:c:s0378437123009238
    DOI: 10.1016/j.physa.2023.129368
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    References listed on IDEAS

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    1. Hidemaro Suwa & Synge Todo, 2011. "Geometric Allocation Approach for Transition Kernel of Markov Chain," Papers 1106.3562, arXiv.org, revised Jul 2012.
    2. Schram, Raoul D. & Barkema, Gerard T., 2015. "Monte Carlo methods beyond detailed balance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 418(C), pages 88-93.
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