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Multicanonical MCMC for sampling rare events: an illustrative review

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  • Yukito Iba
  • Nen Saito
  • Akimasa Kitajima

Abstract

Multicanonical MCMC (Multicanonical Markov Chain Monte Carlo; Multicanonical Monte Carlo) is discussed as a method of rare event sampling. Starting from a review of the generic framework of importance sampling, multicanonical MCMC is introduced, followed by applications in random matrices, random graphs, and chaotic dynamical systems. Replica exchange MCMC (also known as parallel tempering or Metropolis-coupled MCMC) is also explained as an alternative to multicanonical MCMC. In the last section, multicanonical MCMC is applied to data surrogation; a successful implementation in surrogating time series is shown. In the appendix, calculation of averages and normalizing constant in an exponential family, phase coexistence, simulated tempering, parallelization, and multivariate extensions are discussed. Copyright The Institute of Statistical Mathematics, Tokyo 2014

Suggested Citation

  • Yukito Iba & Nen Saito & Akimasa Kitajima, 2014. "Multicanonical MCMC for sampling rare events: an illustrative review," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(3), pages 611-645, June.
    • Handle: RePEc:spr:aistmt:v:66:y:2014:i:3:p:611-645
    DOI: 10.1007/s10463-014-0460-2
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    References listed on IDEAS

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    Cited by:

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    2. Shintaro Nagata & Macoto Kikuchi, 2020. "Emergence of cooperative bistability and robustness of gene regulatory networks," PLOS Computational Biology, Public Library of Science, vol. 16(6), pages 1-24, June.

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