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- W3058599000 abstract "Quasi-Monte Carlo (QMC) points are a substitute for plain Monte Carlo (MC) points that greatly improve integration accuracy under mild assumptions on the problem. Because QMC can give errors that are o(1/n) as $$nrightarrow infty $$ , and randomized versions can attain root mean squared errors that are o(1/n), changing even one point can change the estimate by an amount much larger than the error would have been and worsen the convergence rate. As a result, certain practices that fit quite naturally and intuitively with MC points can be very detrimental to QMC performance. These include thinning, burn-in, and taking sample sizes such as powers of 10, when the QMC points were designed for different sample sizes. This article looks at the effects of a common practice in which one skips the first point of a Sobol’ sequence. The retained points ordinarily fail to be a digital net and when scrambling is applied, skipping over the first point can increase the numerical error by a factor proportional to $$sqrt{n}$$ where n is the number of function evaluations used." @default.
- W3058599000 created "2020-08-24" @default.
- W3058599000 creator A5035543011 @default.
- W3058599000 date "2022-01-01" @default.
- W3058599000 modified "2023-09-25" @default.
- W3058599000 title "On Dropping the First Sobol’ Point" @default.
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- W3058599000 doi "https://doi.org/10.1007/978-3-030-98319-2_4" @default.
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