  ``Extended Ensemble Monte Carlo''is a generic term that indicates a set of
algorithms which are now popular in a variety of fields in physics and
statistical information processing. Exchange Monte Carlo (Metropolis-Coupled
Chain, Parallel Tempering), Simulated Tempering (Expanded Ensemble Monte
Carlo), and Multicanonical Monte Carlo (Adaptive Umbrella Sampling) are typical
members of this family. Here we give a cross-disciplinary survey of these
algorithms with special emphasis on the great flexibility of the underlying
idea. In Sec.2, we discuss the background of Extended Ensemble Monte Carlo. In
Sec.3, 4 and 5, three types of the algorithms, i.e., Exchange Monte Carlo,
Simulated Tempering, Multicanonical Monte Carlo are introduced. In Sec.6, we
give an introduction to Replica Monte Carlo algorithm by Swendsen and Wang.
Strategies for the construction of special-purpose extended ensembles are
discussed in Sec.7. We stress that an extension is not necessary restricted to
the space of energy or temperature. Even unphysical (unrealizable)
configurations can be included in the ensemble, if the resultant fast mixing of
the Markov chain offsets the increasing cost of the sampling procedure.
Multivariate (multi-component) extensions are also useful in many examples. In
Sec.8, we give a survey on extended ensembles with a state space whose
dimensionality is dynamically varying. In the appendix, we discuss advantages
and disadvantages of three types of extended ensemble algorithms.
