Monte Carlo Method - Definition
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Academic Research on Monte Carlo Method TheMonte Carlo methodfor the solution of charge transport in semiconductors with applications to covalent materials, Jacoboni, C., & Reggiani, L. (1983). The Monte Carlo method for the solution of charge transport in semiconductors with applications to covalent materials.Reviews of modern Physics,55(3), 645. This review presents in a comprehensive and tutorial form the basic principles of the Monte Carlo method, as applied to the solution of transport problems in semiconductors. A collection of results obtained with Monte Carlo simulations is presented, with the aim of showing the power of the method in obtaining physical insights into the processes under investigation. Themonte carlo method, Metropolis, N., & Ulam, S. (1949). The monte carlo method.Journal of the American statistical association,44(247), 335-341. ExchangeMonte Carlo methodand application to spin glass simulations, Hukushima, K., & Nemoto, K. (1996). Exchange Monte Carlo method and application to spin glass simulations.Journal of the Physical Society of Japan,65(6), 1604-1608. This study proposes an efficient Monte Carlo algorithm for simulating a ``hardly-relaxing" system, in which many replicas with different temperatures are simultaneously simulated and a virtual process exchanging configurations of these replica is introduced. Monte Carlo Method. Metropolis, N. (1989). Monte Carlo Method.From Cardinals to Chaos: Reflection on the Life and Legacy of Stanislaw Ulam, 125. TheMonte Carlo Method, Sobol, I. M. (1974). The Monte Carlo Method. Markov chainMonte Carlo methodand its application, Brooks, S. (1998). Markov chain Monte Carlo method and its application.Journal of the royal statistical society: series D (the Statistician),47(1), 69-100. This paper provides a simple, comprehensive and tutorial review of some of the most common areas of research of the use of the Markov Chain Monte Carlo (MCMC) method as a statistical tool. The study proposes how MCMC algorithms can be constructed from standard building-blocks to produce Markov chains with the desired stationary distribution. It also discusses some implementational issues associated with MCMC methods. A practical manual on theMonte Carlo methodfor random walk problems, Cashwell, E. D., & Everett, C. J. (1959). A practical manual on the Monte Carlo method for random walk problems. This report is written to serve as a guide to those persons who, having no previous experience with Monte Carlo methods, wish to apply these methods to their own problems. Included as an appendix are brief summaries of a variety of problems of the above-mentioned type to which the methods described have been applied successfully. AMonte Carlo methodfor factorization, Pollard, J. M. (1975). A Monte Carlo method for factorization.BIT Numerical Mathematics,15(3), 331-334. This study discusses briefly a novel factorization method involving probabilistic ideas. Matrix inversion by aMonte Carlo method, Forsythe, G. E., & Leibler, R. A. (1950). Matrix inversion by a Monte Carlo method.Mathematics of Computation,4(31), 127-129. A regression-basedMonte Carlo methodto solve backward stochastic differential equations, Gobet, E., Lemor, J. P., & Warin, X. (2005). A regression-based Monte Carlo method to solve backward stochastic differential equations.The Annals of Applied Probability,15(3), 2172-2202. This paper is concerned with the numerical resolution of backward stochastic differential equations. The paper proposes a new numerical scheme based on iterative regressions on function bases, which coefficients are evaluated using Monte Carlo simulations. Numerical experiments about finance are included, in particular, concerning option pricing with differential interest rates. An adaptive sequentialMonte Carlo methodfor approximate Bayesian computation, Del Moral, P., Doucet, A., & Jasra, A. (2012). An adaptive sequential Monte Carlo method for approximate Bayesian computation.Statistics and Computing,22(5), 1009-1020. In this article, an adaptive sequential Monte Carlo (SMC) algorithm is proposed which admits a computational complexity that is linear in the number of samples and adaptively determines the simulation parameters for Markov chain Monte Carlo method (MCMC). The paper demonstrates its algorithm on a toy example and on a birth-death-mutation model arising in epidemiology.