The average dimension of a multidimensional function for quasi-Monte Carlo estimates of an integral

Asotsky, D. I.; Myshetskaya, E. E.; Sobol, I. M.

doi:10.1134/s0965542506120050

Cited by 10 publications

(5 citation statements)

References 9 publications

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“…where m Ӷ d. Obviously, the ANOVA decomposition of (1.1) contains lowdimensional terms only: their dimensions cannot exceed m. Therefore, the average dimension of (1.1) also does not exceed m. The concept of average dimension was introduced by A. Owen in Liu and Owen (2006) and independently by Asotsky et al (2006). These papers contain an important suggestion: for integrands with small average dimension, QMC integrations are superior to MC integrations.…”

Section: Technical Papermentioning

confidence: 99%

Construction and Comparison of High-Dimensional Sobol' Generators

Sobol¹,

Asotsky²,

Kreinin³

et al. 2011

Wilmott

168

106

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Sobol' sequence generators are used actively in financial applications. In this paper, we explore the effect of the uniformity Properties A and A' on the generator performance in high-dimensional problems. It is shown that these properties provide an additional guarantee of uniformity for highdimensional problems even at a small number of sampled points. By imposing additional uniformity properties on low-dimensional projections of the sequence in addition to the uniformity properties of the d-dimensional sequence itself, the efficiency of the Sobol' sequence can be increased. The SobolSeq16384 generator, which satisfies additional uniformity properties (Property A for all 16,384 dimensions and Property A' for adjacent dimensions), is constructed. A comparison of known Sobol' sequence generators for a set of tests shows that for the majority of tests, the SobolSeq16384 generator performs better than other generators.

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Section: Technical Papermentioning

confidence: 99%

Construction and Comparison of High-Dimensional Sobol' Generators

Sobol¹,

Asotsky²,

Kreinin³

et al. 2011

Wilmott

168

106

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“…A year later the same concept was introduced in [1]. The integrals below are written without integration limits because all the variables vary independently from 0 to 1.…”

Section: A Appendixmentioning

confidence: 97%

Quasi-Monte Carlo: A high-dimensional experiment

Sobol¹,

Shukhman²

2014

Monte Carlo Methods and Applications

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“…The use of such quasirandom sampling for numerical integration is referred to as "quasi-Monte Carlo" integration. Quasirandom sampling based on "scrambled nets" [18][19][20][21][22] has the property that, for "well-behaved" functions, the error becomes proportional to −3/2 log /2 , which is much less than the 1/( √ ) for traditional Monte Carlo integration. Section 5 will discuss quasi-Monte Carlo methods.…”

Section: Simulation For the Design Of Nanoscale Vlsi Circuitsmentioning

confidence: 99%

Computational Performance Optimisation for Statistical Analysis of the Effect of Nano-CMOS Variability on Integrated Circuits

Xie

Edwards

2013

VLSI Design

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The intrinsic variability of nanoscale VLSI technology must be taken into account when analyzing circuit designs to predict likely yield. Monte-Carlo- (MC-) and quasi-MC- (QMC-) based statistical techniques do this by analysing many randomised or quasirandomised copies of circuits. The randomisation must model forms of variability that occur in nano-CMOS technology, including “atomistic” effects without intradie correlation and effects with intradie correlation between neighbouring devices. A major problem is the computational cost of carrying out sufficient analyses to produce statistically reliable results. The use of principal components analysis, behavioural modeling, and an implementation of “Statistical Blockade” (SB) is shown to be capable of achieving significant reduction in the computational costs. A computation time reduction of 98.7% was achieved for a commonly used asynchronous circuit element. Replacing MC by QMC analysis can achieve further computation reduction, and this is illustrated for more complex circuits, with the results being compared with those of transistor-level simulations. The “yield prediction” analysis of SRAM arrays is taken as a case study, where the arrays contain up to 1536 transistors modelled using parameters appropriate to 35 nm technology. It is reported that savings of up to 99.85% in computation time were obtained.

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The average dimension of a multidimensional function for quasi-Monte Carlo estimates of an integral

Cited by 10 publications

References 9 publications

Construction and Comparison of High-Dimensional Sobol' Generators

Construction and Comparison of High-Dimensional Sobol' Generators

Quasi-Monte Carlo: A high-dimensional experiment

Computational Performance Optimisation for Statistical Analysis of the Effect of Nano-CMOS Variability on Integrated Circuits

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