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On the asymptotic variance of reversible Markov chain without cycles

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  • Wu, Chi-Hao
  • Chen, Ting-Li

Abstract

Markov chain Monte Carlo(MCMC) is a popular approach to sample from high dimensional distributions, and the asymptotic variance is a commonly used criterion to evaluate the performance. While most popular MCMC algorithms are reversible, there is a growing literature on the development and analyses of nonreversible MCMC. Chen and Hwang (2013) showed that a reversible MCMC can be improved by adding an antisymmetric perturbation. They also raised a conjecture that it cannot be improved if there is no cycle in the corresponding graph. In this paper, we present a rigorous proof of this conjecture. The proof is based on the fact that the transition matrix with an acyclic structure will produce minimum commute time between vertices.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:137:y:2018:i:c:p:224-228
    DOI: 10.1016/j.spl.2018.01.020
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    References listed on IDEAS

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    1. Chen, Ting-Li & Hwang, Chii-Ruey, 2013. "Accelerating reversible Markov chains," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 1956-1962.
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    Cited by:

    1. Hua, Chen-Wei & Chen, Ting-Li, 2022. "On multiple acceleration of reversible Markov chain," Statistics & Probability Letters, Elsevier, vol. 189(C).

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