Empirical convergence bounds for quasi-monte carlo integration
Abstract
A possibility of a probabilistic approach to a deterministic error estimation procedure of quasi-Monte-Carlo method is presented. Existing estimation methods of the aforementioned estimation are non-constructive. A well-known Koksma-Hlawka inequality includes a constant integrand variation, estimation of which is a more complex problem. Since quasi Monte-Carlo method estimates the integral with the mean integrand value, we can expect that the error distribution (in a probabilistic sense) converges to normal. An additional difficulty, however, is that quasi-random sequences, being treated as randomly generated, are statistically dependent, which complicates the numerical estimation of second moments. Authors propose a new approach to the problem of estimating second order moments, based on new results, derived from a theory of random cubature formulas. Presented numerical examples indicate the superiority of the discussed error estimation method over classical ones. Refs 0. Figs 0. Tables 0.Keywords:
Monte Carlo and Quasi-Monte Carlo method, confidence interval, random cubature formulas, Haar functions, Sobol sequences
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Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.