Multicanonical MCMC for Sampling Rare Events

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 appendices, calculation of averages and normalizing constant in an exponential family, phase coexistence, simulated tempering, parallelization, and multivariate extensions are discussed.

Presented at BayesComp2012;in the journal format (NOT a4 size); Major revised from the previous Arxiv version. Fig.3 and Fig.13(Fig.12 old) is revised and Fig.6 is added. Sec.2.2.5 is added. Results in Sec.4.2.3 are substituted, including figures. Many other important changes. A typo in the publication version is corrected; in the footnote 15, Q_{opt} should be replaced by Q_*. The final publication is available at springerlink.com http://link.springer.com/article/10.1007%2Fs10463-014-0460-2

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