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Erschienen in:
2010 | OriginalPaper | Buchkapitel
Independent Monte Carlo
verfasst von : Kenneth Lange
Erschienen in: Numerical Analysis for Statisticians
Verlag: Springer New York
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Monte Carlo integration is a rough and ready technique for calculating high-dimensional integrals and dealing with nonsmooth integrands [4, 5, 6, 8, 9, 10, 11, 12, 13]. Although quadrature methods can be extended to multiple dimensions, these deterministic techniques are almost invariably defeated by the curse of dimensionality. For example, if a quadrature method relies on
n
quadrature points in one dimension, then its product extension to
d
dimensions relies on
n
d
quadrature points. Even in one dimension, quadrature methods perform best for smooth functions. Both Romberg acceleration and Gaussian quadrature certainly exploit smoothness.