Extended ensemble Monte Carlo

"Extended Ensemble Monte Carlo" is a generic term that indicates a set of a lgorithms, which are now popular in a variety of fields in physics and stat istical information processing. Exchange Monte Carlo (Metropolis-Coupled Ch ain, Parallel Tempering), Simulated Tempering (Expanded Ensemble Monte Carl o) and Multicanonical Monte Carlo (Adaptive Umbrella Sampling) axe 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 Carl o. In Sees. 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 Swends en and Wang. Strategies for the construction of special-purpose extended en sembles are discussed in Sec. 7. We stress that an extension is not necessa ry restricted to the space of energy or temperature. Even unphysical (unrea lizable) configurations can be included in the ensemble, if the resultant f ast mixing of the Markov chain offsets the increasing cost of the sampling procedure. Multivariate (multicomponent) extensions are also useful in many examples. In Sec. 8, we give a survey on extended ensembles with a state s pace whose dimensionality is dynamically varying. In the appendix, we discu ss advantages and disadvantages of three types of extended ensemble algorit hms.