This study presents improved understanding of sensitivity analysis methods through a comparison of the local sensitivity and two global sensitivity analysis methods: the Morris and Sobol′/Saltelli methods. We re-interpret the variance-based sensitivity indices from the Sobol′/Saltelli method as difference-based measures. It suggests that the difference-based local and Morris methods provide the...

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 method of derivative based global sensitivity measures (DGSM) has recently become popular among practitioners. It has a strong link with the Morris screening method and Sobol’ sensitivity indices and has several advantages over them. DGSM are very easy to implement and evaluate numerically. The computational time required for numerical evaluation of DGSM is generally much lower than that fo...

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...

Monte Carlo simulation is widely used to price complex nancial instruments. Recent theoretical results and extensive computer testing indicate that deterministic methods may be far superior in speed and conndence. Simulations using the Sobol or Faure points are examples of deterministic methods. For the sake of brevity, we refer to a deterministic method using the name of the sequence of points...

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...

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...