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 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...

Global sensitivity analysis is widely used in many areas of science, biology, sociology and policy planning. The variance-based methods also known as Sobol' sensitivity indices has become the method of choice among practitioners due to its efficiency and ease of interpretation. For complex practical problems, estimation of Sobol' sensitivity indices generally requires a large number of function...

A novel theoretical and numerical framework for the estimation of Sobol ’ sensitivity indices for models in which inputs are confined to a non-rectangular domain (e.g., in presence of inequality constraints) is developed. Two numerical methods, namely the quadrature integration method which may be very efficient for problems of low dimensionality and the MC/QMC estimators based on the acceptanc...

Sobol’ indices measure the dependence of a high dimensional function on groups of variables defined on the unit cube [0, 1]. They are based on the ANOVA decomposition of functions, which is an L decomposition. In this paper we discuss generalizations of Sobol’ indices which yield L measures of the dependence of f on subsets of variables. Our interest is in values p > 2 because then variable imp...