Concepts and implementation of the Cuba library for multidimensional numerical integration are elucidated. 1. Overview Cuba [1] is a library for multidimensional numerical integration. It features four integration algorithms with interfaces for Fortran, C/C++, and Mathematica. All four can integrate vector integrands and their invocation is quite similar to make it easy to switch routines for c...

The global sensitivity analysis of a complex numerical model often calls for the estimation of variance-based importance measures, named Sobol’ indices. Metamodelbased techniques have been developed in order to replace the cpu time-expensive computer code with an inexpensive mathematical function, which predicts the computer code output. The common metamodel-based sensitivity analysis methods a...

Rendering quality is largely influenced by the samplers used in Monte Carlo integration. Important factors include sample uniformity (e.g., low discrepancy) high-dimensional integration domain, lower-dimensional projections, and lack of dominant structures that could result aliasing artifacts. A widely successful construction Sobol' sequence guarantees good consequently results faster convergen...

The minimum distance of QMC sample points to the boundary of the unit cube is an important quantity in the error analysis of QMC integration for functions with singularities. Sobol’ and recently Owen show that the Sobol’ and Halton sequences avoid a hyperbolically shaped region around the corners of the unit cube. We extend these results in two ways. First, we prove that generalized Niederreite...

Global sensitivity analysis of complex numerical models can be performed by calculating variance-based importance measures of the input variables, such as the Sobol indices. However, these techniques, requiring a large number of model evaluations, are often unacceptable for time expensive computer codes. A well known and widely used decision consists in replacing the computer code by a metamode...

nanotechnology involves the ability to see and control individual atoms and molecules which are about 100 nanometer or smaller. one of the major tools used in this field is atomic force microscopy which uses a wealth of techniques to measure the topography and investigates the surface forces in nanoscale. friction force is the representation of the surface interaction between two surfaces an...

In this paper, we study the geometric generation of the (0; m; 2)-nets. Based on some combinatorial methods, a generation property on (0; m; 2)-nets with an applications to a Sobol' sequence and the number of the (0; m; 2)-nets in equivalent sense are given. We also present some symmetry properties of the Sobol' sequence and the Roth-Zaremba sequence.

This paper deals with global sensitivity analysis of computer model output. Given a set of independent input sample and associated model output vector with possibly the vector of output derivatives with respect to the input variables, we show that it is possible to evaluate the following global sensitivity measures: (i) the Sobol’ indices, (ii) the Borgonovo’s density-based sensitivity measure,...

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...