Multicanonical MCMC for Sampling Rare Events

TL;DR

This paper reviews multicanonical MCMC as a method for sampling rare events, discusses its applications in various fields, compares it with replica exchange MCMC, and demonstrates its use in time series surrogation.

Contribution

It provides a comprehensive overview of multicanonical MCMC, including theoretical foundations, practical applications, and extensions, highlighting its effectiveness in rare event sampling.

Findings

Successful application in time series surrogation

Comparison with replica exchange MCMC

Discussion of multicanonical MCMC extensions

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.