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Monte Carlo Method

A Monte Carlo method solves a problem by generating suitable random numbers and using the resulting sample values to estimate an answer. For example, the fraction of samples satisfying a specified property estimates the corresponding probability. 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.

The corresponding deterministic analog, in which random samples are replaced by carefully selected points, is a quasi-Monte Carlo method.

See also

Markov Chain, Monte Carlo Integration, Quasi-Monte Carlo Method, Stochastic Geometry, Uniform Distribution Theory

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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. "The Beginning of the Monte Carlo Method." Los Alamos Science, No. 15, p. 125. http://jackman.stanford.edu/mcmc/metropolis1.pdf.Metropolis, N. and Ulam, S. "The Monte Carlo Method." J. Amer. Stat. Assoc. 44, 335-341, 1949.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.

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Monte Carlo Method

Cite this as:

Weisstein, Eric W. "Monte Carlo Method." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MonteCarloMethod.html

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