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Quasi-Monte Carlo Method

A quasi-Monte Carlo method is a deterministic analog of a Monte Carlo method in which random samples are replaced by carefully selected points. The points are commonly obtained from quasirandom sequences and are chosen to cover the relevant domain more evenly than independent random points (Niederreiter 1992).

The appropriate measure of point-set quality depends on the problem being solved. In quasi-Monte Carlo integration, the principal criterion is low discrepancy. For global optimization, the analogous deterministic search instead seeks point sets with small dispersion (Niederreiter 1992). Thus quasi-Monte Carlo integration is the most prominent instance of a broader class of methods.

See also

Discrepancy, Global Optimization, Monte Carlo Method, Quasi-Monte Carlo Integration, Quasirandom Number, Quasirandom Sequence, Uniform Distribution Theory

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References

Drmota, M. and Tichy, R. F. Sequences, Discrepancies and Applications. New York: Springer-Verlag, 1997.Hellekalek, P. and Larcher, G. (Eds.). Random and Quasi-Random Point Sets. New York: Springer-Verlag, 1998.Kuipers, L. and Niederreiter, H. Uniform Distribution of Sequences. New York: Wiley, 1974.MathConsult Dr. R. Mäder. "QR Streams." http://www.mathdirect.com/products/qrn/.Niederreiter, H. Random Number Generation and Quasi-Monte Carlo Methods. Philadelphia, PA: SIAM, 1992.

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Quasi-Monte Carlo Method

Cite this as:

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

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