  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.
