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Dynamic Monte Carlo method
About: Dynamic Monte Carlo method is a research topic. Over the lifetime, 13294 publications have been published within this topic receiving 371256 citations.
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TL;DR: In this paper, a brief general introduction on the nature of Monte Carlo methods that can be skipped by readers acquainted with them is given, and the application of these methods to multivariable problems is discussed.
Abstract: This paper opens with a brief general introduction on the nature of Monte Carlo methods that can be skipped by readers acquainted with them. I then deal more specifically with the application of these methods to multivariable problems, and I indicate certain relatively unexplored areas of this field where further research might be profitable. As I believe is appropriate, some of my material is exploratory, speculative, and controversial, and accordingly I hope it will stimulate discussion.
497 citations
TL;DR: The Monte Carlo approach to testing a simple null hypothesis is reviewed briefly and several examples of its application to problems involving spatial distributions are presented, to illustrate the value of the general approach, particularly at a preliminary stage of analysis.
Abstract: The Monte Carlo approach to testing a simple null hypothesis is reviewed briefly and several examples of its application to problems involving spatial distributions are presented. These include spatial point pattern, pattern similarity, space‐time interaction and scales of pattern. The aim is not to present specific “recommended tests” but rather to illustrate the value of the general approach, particularly at a preliminary stage of analysis.
493 citations
TL;DR: In this paper, the authors compared the performance of quasi-random and random Monte Carlo methods for multidimensional integrals with respect to variance, variation, smoothness, and dimension.
492 citations
TL;DR: In this article, the authors proposed modifications to the simple diffusion Monte Carlo algorithm that greatly reduce the time step error and achieved a time-step error smaller by a factor of 70 to 300 in the energy of Be, Li2 and Ne.
Abstract: We propose modifications to the simple diffusion Monte Carlo algorithm that greatly reduce the time‐step error. The improved algorithm has a time‐step error smaller by a factor of 70 to 300 in the energy of Be, Li2 and Ne. For other observables the improvement is yet larger. The effective time step possible with the improved algorithm is typically a factor of a few hundred larger than the time step used in domain Green function Monte Carlo. We also present an optimized 109 parameter trial wave function for Be which, used in combination with our algorithm, yields an exceedingly accurate ground state energy. A simple solution to the population control bias in diffusion Monte Carlo is also discussed.
488 citations
01 Jan 1995
TL;DR: The book is mainly concerned with the mathematical foundations of Bayesian image analysis and its algorithms, which amounts to the study of Markov random fields and dynamic Monte Carlo algorithms like sampling, simulated annealing and stochastic gradient algorithms.
486 citations