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Randomly permuted \((t,m,s)\)-nets and \((t,s)\)-sequences. (English) Zbl 0831.65024

Niederreiter, Harald (ed.) et al., Monte Carlo and quasi-Monte Carlo methods in scientific computing. Proceedings of a conference at the University of Nevada, Las Vegas, Nevada, USA, June 23-25, 1994. Berlin: Springer-Verlag. Lect. Notes Stat. 106, 299-317 (1995).
Summary: This article presents a hybrid of Monte Carlo and quasi-Monte Carlo methods. In this hybrid, certain low discrepancy point sets and sequences due to Faure, Niederreiter and Sobol’ are obtained and their digits are randomly permuted. Since this randomization preserves the equidistribution properties for the points it also preserves the proven bounds on their quadrature errors. The accuracy of an estimated integrand can be assessed by replication, consisting of independent re- randomizations.
The hybrid method is applied to two published sets of test integrands. The results on the larger set of test integrands suggest that the randomized sequences tend to give more accurate integral estimates than the original unpermuted points.
The method presented here is a further step in a sequence of methods from the statistical literature, that starts with Latin hypercube sampling and develops through randomized orthogonal arrays and orthogonal array based Latin hypercube sampling.
For the entire collection see [Zbl 0827.00048].

MSC:

65D32 Numerical quadrature and cubature formulas
65C05 Monte Carlo methods
11K45 Pseudo-random numbers; Monte Carlo methods
11K38 Irregularities of distribution, discrepancy
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