On the asymptotic distribution of scrambled net quadrature

Loh, Wei-Liem

doi:10.1214/aos/1059655914

Cited by 52 publications

(60 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Here we take a single quasirandom sequence and provide different random digit scramblings of the given sequence. If the scrambling preserves certain equidistribution properties of the parent sequence, then the result will be high-quality quasirandom numbers for each parallel process, and an overall successful parallel quasi-Monte Carlo computation as expected from the Koksma-Hlawka inequality [11].…”

Section: Parallelization and Implementationsmentioning

confidence: 99%

Efficient Generation of Parallel Quasirandom Faure Sequences Via Scrambling

Chi

Mascagni

2007

Computational Science – ICCS 2007

View full text Add to dashboard Cite

Abstract. Much of the recent work on parallelizing quasi-Monte Carlo methods has been aimed at splitting a quasirandom sequence into many subsequences which are then used independently on the various parallel processes. This method works well for the parallelization of pseudorandom numbers, but due to the nature of quality in quasirandom numbers, this technique has many drawbacks. In contrast, this paper proposes an alternative approach for generating parallel quasirandom sequences via scrambling. The exact meaning of the digit scrambling we use depends on the mathematical details of the quasirandom number sequence's method of generation. The Faure sequence is scramble by modifying the generator matrices in the definition. Thus, we not only obtain the expected near-perfect speedup of the naturally parallel Monte Carlo methods, but the errors in the parallel computation is even smaller than if the computation were done with the same quantity of quasirandom numbers using the original Faure sequence.

show abstract

Section: Parallelization and Implementationsmentioning

confidence: 99%

Efficient Generation of Parallel Quasirandom Faure Sequences Via Scrambling

Chi

Mascagni

2007

Computational Science – ICCS 2007

View full text Add to dashboard Cite

show abstract

“…The limiting distribution of an RQMC estimator based on a randomly-shifted lattice rule when n → ∞ is analyzed in [38]; the properly scaled limiting distribution is usually a spline, not a normal distribution. For a digital net with a digital random shift, the CLT does not apply either (in one dimension it is equivalent to a randomly-shifted lattice), but the CLT does apply for a digital net with NUS [45].…”

Section: A Stochastic Activity Networkmentioning

confidence: 99%

“…This can be used to estimate the integration error. It may seem natural to compute a confidence interval by assuming thatX m is approximately normally distributed, but one should be careful: The CLT holds in general for m → ∞, but for fixed m and n → ∞ it holds only for a few RQMC methods [38,45]. When applying RQMC to estimate µ, for a given total computing budget mn, we prefer n as large as possible to benefit from the faster convergence rate in n, and then m is small (e.g., 10 or 20) andX m may be far from normally distributed.…”

Section: Introductionmentioning

confidence: 99%

Randomized Quasi-Monte Carlo: An Introduction for Practitioners

L’Ecuyer

2018

Springer Proceedings in Mathematics &Amp; Statistics

View full text Add to dashboard Cite

We survey basic ideas and results on randomized quasi-Monte Carlo (RQMC) methods, discuss their practical aspects, and give numerical illustrations. RQMC can improve accuracy compared with standard Monte Carlo (MC) when estimating an integral interpreted as a mathematical expectation. RQMC estimators are unbiased and their variance converges at a faster rate (under certain conditions) than MC estimators, as a function of the sample size. Variants of RQMC also work for the simulation of Markov chains, for function approximation and optimization, for solving partial differential equations, etc. In this introductory survey, we look at how RQMC point sets and sequences are constructed, how we measure their uniformity, why they can work for high-dimensional integrals, and how can they work when simulating Markov chains over a large number of steps.

show abstract

“…Quasirandom sequences are more suitable for such applications. In particular, fewer quasi-random samples are needed to achieve a similar level of accuracy as obtained by using pseudo-random sequences [11,18].…”

Section: Quasirandom Sequencesmentioning

confidence: 99%

Generating Test Data for Specification-Based Tests Via Quasirandom Sequences

Chi

Jones

Evans

et al. 2006

Computational Science – ICCS 2006

View full text Add to dashboard Cite

Abstract. This paper presents work on generation of specificationdriven test data, by introducing techniques based on a subset of quasirandom sequences (completely uniformly distributed sequences) to generate test data. This approach is novel in software testing. This enhanced uniformity of quasirandom sequences leads to faster generation of test data covering all possibilities. We demonstrate by examples that welldistributed sequences can be a viable alternative to pseudorandom numbers in generating test data. In this paper, we present a method that can generate test data from a decision table specification more effectively via quasirandom numbers. Analysis of a simple problem in this paper shows that quasirandom sequences achieve better data than pseudorandom numbers, and have the potential to converge faster and so reduce the computational burden. Functional test coverage, an objective criteria, evaluates the quality of a test set to ensure that all specified behaviors will be exercised by the test data.

show abstract

On the asymptotic distribution of scrambled net quadrature

Cited by 52 publications

References 20 publications

Efficient Generation of Parallel Quasirandom Faure Sequences Via Scrambling

Efficient Generation of Parallel Quasirandom Faure Sequences Via Scrambling

Randomized Quasi-Monte Carlo: An Introduction for Practitioners

Generating Test Data for Specification-Based Tests Via Quasirandom Sequences

Contact Info

Product

Resources

About