Problems in many disciplines, such as physics, chemistry, and finance, can be modelled as integrals of high dimensions (hundreds or even thousands). Quasi-Monte Carlo (QMC) methods, which perform sampling using a more uniform point set than that used in MC, have been successfully used to approximate multivariate integrals with an error bound of size O((logN)kN−1) or even O((logN)kN−3/2), where ...

A standard assumption in stated preferences modelling is the independence between repeated responses from an interviewee. The rationale for this strong assumption is that the mathematical treatment of the choices becomes rather cumbersome when dependency is incorporated in the analysis. Assuming dependence between the various responses given by one individual is known as the repeated observatio...

Hybrids of equidistribution and Monte Carlo methods of integration can achieve the superior accuracy of the former while allowing the simple error estimation methods of the latter. In particular randomized (0; m; s)-nets in base b produce unbiased estimates of the integral, have a variance that tends to zero faster than 1=n for any square integrable integrand, and have a variance that for nite ...

In the field of sensitivity analysis, Sobol’ indices are widely used to assess importance inputs a model its output. Among methods that estimate these indices, replication procedure is noteworthy for efficient cost. A practical problem how many evaluations must be performed guarantee sufficient precision on estimates. The present paper tackles this issue by rendering iterative. idea enable addi...

This paper presents a parallelized Quasi-Monte Carlo algorithm for the extraction of partial inductances in IC interconnect structures. Quasi-random numbers provide superior convergence over pseudo-random numbers, and in this paper the results are presented for three quasi-random number sequences-Halton, Sobol and Niderreiter. The algorithm has been parallelized and an almost linear rate of par...