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Accelerating reversible Markov chains

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  • Chen, Ting-Li
  • Hwang, Chii-Ruey

Abstract

Reversibility is usually applied in most popular Markov chain Monte Carlo algorithms, such as the Metropolis–Hastings algorithm and the Gibbs sampler. However, several researchers have shown that non-reversible Markov chains are better than reversible ones. In this paper, we present a method for accelerating a reversible Markov chain. For any reversible Markov chain with a cycle on the corresponding graph, we construct a non-reversible Markov chain by adding some antisymmetric perturbations to the original chain. We prove that this non-reversible Markov chain is uniformly better than the original one in the sense of having a smaller asymptotic variance. Furthermore, we propose a conjecture that no uniformly better chain exists for the acyclic case.

Suggested Citation

  • Chen, Ting-Li & Hwang, Chii-Ruey, 2013. "Accelerating reversible Markov chains," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 1956-1962.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:9:p:1956-1962
    DOI: 10.1016/j.spl.2013.05.002
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    Citations

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    Cited by:

    1. Wu, Chi-Hao & Chen, Ting-Li, 2018. "On the asymptotic variance of reversible Markov chain without cycles," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 224-228.
    2. Belmabrouk, Nadia & Damak, Mondher & Yaakoubi, Nejib, 2022. "Dirichlet eigenvalue problems of irreversible Langevin diffusion," Statistics & Probability Letters, Elsevier, vol. 180(C).
    3. Hua, Chen-Wei & Chen, Ting-Li, 2022. "On multiple acceleration of reversible Markov chain," Statistics & Probability Letters, Elsevier, vol. 189(C).
    4. Marie Vialaret & Florian Maire, 2020. "On the Convergence Time of Some Non-Reversible Markov Chain Monte Carlo Methods," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 1349-1387, September.
    5. Manal Dakil & Christophe Simon & Taha Boukhobza, 2014. "Reliability and availability analysis of the structural observability of bilinear systems: A graph-theoretical approach," Journal of Risk and Reliability, , vol. 228(3), pages 218-229, June.
    6. Hwang, Chii-Ruey & Normand, Raoul & Wu, Sheng-Jhih, 2015. "Variance reduction for diffusions," Stochastic Processes and their Applications, Elsevier, vol. 125(9), pages 3522-3540.
    7. Shiu, Shang-Ying & Chen, Ting-Li, 2015. "On the rate of convergence of the Gibbs sampler for the 1-D Ising model by geometric bound," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 14-19.

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