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.In this paper, we will give a survey on Extended Ensemble Monte Carlo algorithms 1 , which are useful tools in computational physics and in the fields of statistical information processing. Well-known algorithms in this family are Exchange Monte Carlo (Metropolis-Coupled Chain, Parallel Tempering) [2,3,4,5,6,7,8], Simulated Tempering (Expanded Ensemble Monte Carlo) [1,9] and Multicanonical Monte Carlo (Adaptive Umbrella Sampling) [10,11,12,13,14]. These approaches are characterized by modification of ensembles sampled by the algorithm. In this respects, they contrast with other attempts to overcome the limitation of conventional Dynamical Monte Carlo, i.e., improved dynamics that preserve original ensembles [15,16] and improved algorithms that maintain original dynamics [17].These algorithms are useful for the studies of stochastic models in various fields of physics, e.

Abstract. "Nishimori line" is a line or hypersurface in the parameter space of systems with quenched disorder, where simple expressions of the averages of physical quantities over the quenched random variables are obtained. It has been playing an important role in the theoretical studies of the random frustrated systems since its discovery around 1980. In this paper, a novel interpretation of the Nishimori line from the viewpoint of statistical information processing is presented. Our main aim is the reconstruction of the whole theory of the Nishimori line from the viewpoint of Bayesian statistics, or, almost equivalently, from the viewpoint of the theory of error-correcting codes. As a byproduct of our interpretation, counterparts of the Nishimori line in models without gauge invariance are given. We also discussed the issues on the "finite temperature decoding" of error-correcting codes in connection with our theme and clarify the role of gauge invariance in this topic.

Long chains of the HP lattice protein model are studied by the multi-self-overlap ensemble Monte Carlo method, which was developed recently by Iba, Chikenji, and Kikuchi. This method successfully finds the lowest energy states reported before for sequences of the chain length N 42 100 in two and three dimensions. Moreover, the method realizes the lowest energy state that was ever found in a case of N 100. Finite-temperature properties of these sequences are also investigated by this method. Two successive transitions are observed between the native and random coil states. Thermodynamic analysis suggests that the ground state degeneracy is relevant to the order of the transitions.

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We give a cross-disciplinary survey on "population" Monte Carlo algorithms. In these algorithms, a set of "walkers" or "particles" is used as a representation of a high-dimensional vector. The computation is carried out by a random walk and split/deletion of these objects. The algorithms are developed in various fields in physics and statistical sciences and called by lots of different terms -"quantum Monte Carlo", "transfermatrix Monte Carlo", "Monte Carlo filter (particle filter)","sequential Monte Carlo" and "PERM" etc. Here we discuss them in a coherent framework. We also touch on related algorithms -genetic algorithms and annealed importance sampling.