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. Gilks, W. R.; Richardson, S.; and Spiegelhalter,
D. J. (Eds.). Markov
Chain Monte Carlo in Practice. Hoffman,
P. The
Man Who Loved Only Numbers: The Story of Paul Erdős and the Search for Mathematical
Truth. Kuipers, L.
and Niederreiter, H. Uniform
Distribution of Sequences. Manno, I. Introduction
to the Monte Carlo Method. 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. 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. Sobol, I. M. A
Primer for the Monte Carlo Method. Referenced
on Wolfram|Alpha Monte Carlo Method
Cite this as:
Weisstein, Eric W. "Monte Carlo Method."
From MathWorld https://mathworld.wolfram.com/MonteCarloMethod.html
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