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 ...

High-dimensional integrals are usually solved with Monte Carlo algorithms although theory suggests that low discrepancy algorithms are sometimes superior. We report on numerical testing which compares low discrepancy and Monte Carlo algorithms on the evaluation of nancial derivatives. The testing is performed on a Collateralized Mortgage Obligation (CMO) which is formulated as the computation o...

The bark of the underground stem of Tontelea micrantha (Mart. ex. Schult.) A. C. Sm., a native Brazilian Cerrado species, is used in folk medicine for treating kidney ailments. The structures of the underground and the aerial stems were examined and their barks were analyzed for the presence of secondary metabolites. Bark fragments were processed according to conventional techniques in plant an...

In most cases, global sensitivity analysis requires sampling a model at a large number of points in the input space (Monte Carlo), which requires a corresponding sample design. In this paper, we investigate the convergence properties of two different quasi-random sampling designs in variancebased sensitivity analysis Sobol’s Quasi-Monte Carlo (LP-tau) approach, and Latin supercube sampling. We ...

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...

In this paper advanced variance-based algorithms for global sensitivity analysis are studied. We consider efficient algorithms: Monte Carlo, quasi-Monte Carlo (QMC) and scrambled quasi-Monte Carlo algorithms based on Sobol sequences. Low discrepancy ΛΠτ Sobol sequences are considered as a basis. Two other approaches are also analyzed. The first one is an efficient Monte Carlo (MC) algorithm for...