Multicanonical MCMC for sampling rare events: an illustrative review |
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Authors: | Yukito Iba Nen Saito Akimasa Kitajima |
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Institution: | 1. The Institute of Statistical Mathematics and SOKENDAI, 10-3 Midori-cho, Tachikawa, Tokyo, 190-8562, Japan 2. Research Center for Complex Systems Biology, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8902, Japan 3. Digital Information Services Division, Digital Information Department, National Diet Library, 1-10-1 Nagata-cho, Chiyoda-ku, Tokyo, 100-8924, Japan
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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. |
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