Scrambling Sobol' and Niederreiter–Xing Points
نویسندگان
چکیده
منابع مشابه
Scrambling Sobol' and Niederreiter-Xing Points
Hybrids of equidistribution and Monte Carlo methods of integration can achieve the superior accuracy of the former while allowing the simple error estimation methods of the latter. In particular randomized (0; m; s)-nets in base b produce unbiased estimates of the integral, have a variance that tends to zero faster than 1=n for any square integrable integrand, and have a variance that for nite ...
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Let f be a finite variance function of d independent input variables. Sobol’ indices are used to measure the importance of input variables and subsets of them. They are based on a variance decomposition. A similar problem arises in economics, when the value produced through the joint efforts of a team is to be attributed to individual members of that team. The Shapley value is widely used to so...
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We introduce a class of functions in d ≥ 3 dimensions which have arbitrary odd superposition effective dimensions between three and d inclusive. We prove that for the integration of any function in this class any Sobol’ points of a fixed length have zero error, whereas Owen’s scrambling of any Sobol’ points of the same length has the same variance of error as simple Monte Carlo methods. Further...
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ژورنال
عنوان ژورنال: Journal of Complexity
سال: 1998
ISSN: 0885-064X
DOI: 10.1006/jcom.1998.0487