Monte Carlo Method
Any method which solves a problem by generating suitable random numbers and observing that fraction of the numbers obeying some property or properties. The method is useful for obtaining numerical solutions to problems which are too complicated to solve analytically. It was named by S. Ulam, who in 1946 became the first mathematician to dignify this approach with a name, in honor of a relative having a propensity to gamble (Hoffman 1998, p. 239). Nicolas Metropolis also made important contributions to the development of such methods.
The most common application of the Monte Carlo method is Monte
Carlo integration.
SEE ALSO: Markov Chain,
Monte Carlo Integration,
Quasi-Monte Carlo Method,
Stochastic Geometry,
Uniform
Distribution Theory
REFERENCES:
Gamerman, D. Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference. Boca Raton,
FL: CRC Press, 1997.
Gilks, W. R.; Richardson, S.; and Spiegelhalter, D. J. (Eds.). Markov
Chain Monte Carlo in Practice. Boca Raton, FL: Chapman & Hall, 1996.
Hoffman, P. The Man Who Loved Only Numbers: The Story of Paul Erdős and the Search for Mathematical
Truth. New York: Hyperion, pp. 238-239, 1998.
Kuipers, L. and Niederreiter, H. Uniform
Distribution of Sequences. New York: Wiley, 1974.
Manno, I. Introduction to the Monte Carlo Method. Budapest, Hungary: Akadémiai Kiadó,
1999.
Metropolis, N. and Ulam, S. "The Monte Carlo Method." J. Amer. Stat.
Assoc. 44, 335-341, 1949.
Metropolis, N. "The Beginning of the Monte Carlo Method." Los Alamos
Science, No. 15, p. 125. http://jackman.stanford.edu/mcmc/metropolis1.pdf.
Mikhailov, G. A. Parametric
Estimates by the Monte Carlo Method. Utrecht, Netherlands: VSP, 1999.
Niederreiter, H. and Spanier, J. (Eds.). Monte Carlo and Quasi-Monte Carlo Methods 1998, Proceedings of a Conference held at the
Claremont Graduate University, Claremont, California, USA, June 22-26, 1998.
Berlin: Springer-Verlag, 2000.
Sobol, I. M. A
Primer for the Monte Carlo Method. Boca Raton, FL: CRC Press, 1994.
Referenced on Wolfram|Alpha:
Monte Carlo Method
CITE THIS AS:
Weisstein, Eric W. "Monte Carlo Method."
From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/MonteCarloMethod.html
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