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 proper...

Let f be a finite variance function of d independent input variables. Sobol’ indices are used to measure the importance of input variables and subsets of them. They are based on a variance decomposition. A similar problem arises in economics, when the value produced through the joint efforts of a team is to be attributed to individual members of that team. The Shapley value is widely used to so...

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 ...

In 1991, Chang and Wu proposed a broadcasting cryptosystem using interpolating polynomials and geometric properties of circles. Nevertheless, the Chang-Wu scheme can be further enforced by using a time-variant parameter and a one-way function to protect legal receivers’ secrets from being disclosed. The authors present an improvement of the Chang-Wu scheme using geometric properties of lines. T...

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...

A novel approach for estimation variance based sensitivity indices for models with dependent variables is presented. Both the first order and total sensitivity indices are derived as generalizations of Sobol’ sensitivity indices. Formulas and Monte Carlo numerical estimates similar to Sobol’ formulas are derived. A copula based approach is proposed for sampling from arbitrary multivariate proba...