Implementation and tests of low-discrepancy sequences

Bratley, Paul; Fox, Bennett L.; Niederreiter, Harald

doi:10.1145/146382.146385

Cited by 224 publications

(154 citation statements)

References 11 publications

Supporting

Mentioning

152

Contrasting

Order By: Relevance

“…Figure 2 shows the convergence rate of the QMC-GF method. We plot the logarithm of the relative error as a function of the logarithm of the sample size for d = 25 and obtain the linear convergence summarized in (8).…”

Section: Methodsmentioning

confidence: 99%

Faster Evaluation of Multidimensional Integrals

Papageorgiou¹,

Traub²

1997

Computers in Physics

View full text Add to dashboard Cite

In a recent paper Keister proposed two quadrature rules as alternatives to Monte Carlo for certain multidimensional integrals and reported his test results. In earlier work we had shown that the quasi-Monte Carlo method with generalized Faure points is very effective for a variety of high dimensional integrals occuring in mathematical finance. In this paper we report test results of this method on Keister's examples of dimension 9 and 25, and also for examples of dimension 60, 80 and 100.For the 25 dimensional integral we achieved accuracy of 10 −2 with less than 500 points while the two methods tested by Keister used more than 220, 000 points. In all of our tests, for n sample points we obtained an empirical convergence rate proportional to n −1 rather than the n −1/2 of Monte Carlo.

show abstract

Section: Methodsmentioning

confidence: 99%

Faster Evaluation of Multidimensional Integrals

Papageorgiou¹,

Traub²

1997

Computers in Physics

View full text Add to dashboard Cite

show abstract

“…the quasi-random simulation of integrals requires significantly less number of simulation points or "draws" relative to the standard Monte-Carlo method (see Morokoff and Caflisch, 1995;Press et al, 1992, Chapter 7;Brately and Fox, 1988;and Bratley et al, 1992).…”

Section: Model Estimation Model Estimation Model Estimation Model Estmentioning

confidence: 99%

“…Krommer and Ueberhuber (1994) provide an extensive review of quasi-random sequences. Among these sequences are those that belong to the family of r-adic expansion of integers: the Halton, Faure, and Sobol sequences (see Bratley et al, 1992 for a good review). In this paper, we will use the Halton sequence in the quasi-Monte Carlo simulation because of its conceptual simplicity.…”

Section: Model Estimation Model Estimation Model Estimation Model Estmentioning

confidence: 99%

A multi-level cross-classified model for discrete response variables

Bhat

2000

Transportation Research Part B: Methodological

View full text Add to dashboard Cite

In many spatial analysis contexts, the variable of interest is discrete and there is spatial clustering of observations. This paper formulates a model that accommodates clustering along more than one dimension in the context of a discrete response variable. For example, in a travel mode choice context, individuals are clustered by both the home zone in which they live as well as by their work locations. The model formulation takes the form of a mixed logit structure and is estimated by maximum likelihood using a combination of Gaussian quadrature and quasiMonte Carlo simulation techniques. An application to travel mode choice suggests that ignoring the spatial context in which individuals make mode choice decisions can lead to an inferior data fit as well as provide inconsistent evaluations of transportation policy measures.

show abstract

“…For a design with n gates, one would need to generate a low-discrepancy sequence with dimensionality of n. Current best low-discrepancy sequence generators offer practical advantage over standard Monte Carlo sequences only in the early r dimensions (r ≤ 12 [16]). Consequently, for efficient parameter variation modeling of circuits, we apply the Karhunen-Loeve Expansion (KLE) [17], a model simplification technique similar to Principle Component Analysis (PCA) [7].…”

Section: Introductionmentioning

confidence: 99%

Efficient parameter variation sampling for architecture simulations

Lü

Joseph

Trajcevski

et al. 2011

2011 Design, Automation &Amp; Test in Europe

View full text Add to dashboard Cite

Abstract-This paper addresses the problem of efficient and effective parameter variation modeling and sampling in computer architecture simulations. While there has been substantial progress in accelerating simulation time for circuit designs subject to manufacturing variations, these approaches are not generally suitable for architectural studies. Toward this we investigated two complementary avenues: (1) adapting low-discrepancy sampling methods for use in Monte Carlo architectural simulations. We apply techniques previously developed for gate-level circuit models to higher level component models and in so doing drastically reduce the number of samples needed for detailed simulation; (2) applying multi-resolution analysis to appropriately decompose geometric regions of a chip, and achieve more effective description of parameter variations without increasing computational complexity. Our experimental results demonstrate that the combined techniques can reduce the number of Monte Carlo trials by a factor of 3.3, maintaining the same accuracy while significantly reducing the overall simulation run-time.

show abstract

Implementation and tests of low-discrepancy sequences

Cited by 224 publications

References 11 publications

Faster Evaluation of Multidimensional Integrals

Faster Evaluation of Multidimensional Integrals

A multi-level cross-classified model for discrete response variables

Efficient parameter variation sampling for architecture simulations

Contact Info

Product

Resources

About