This paper introduces generalized Sobol’ indices, compares strategies for their estimation, and makes a systematic search for efficient estimators. Of particular interest are contrasts, sums of squares and indices of bilinear form which allow a reduced number of function evaluations compared to alternatives. The bilinear framework includes some efficient estimators from Saltelli (2002) and Maun...

Complex environmental models are controlled by a high number of parameters. Accurately estimating the values of all these parameters is almost impossible. Sensitivity analysis (SA) results enable the selection of the parameters to include in a calibration procedure, but can also assist in the identification of the model processes. Additionally, a sensitivity analysis can yield crucial informati...

The presence of uncertainties are inevitable in engineering design and analysis, where failure in understanding their effects might lead to the structural or functional failure of the systems. The role of global sensitivity analysis in this aspect is to quantify and rank the effects of input random variables and their combinations to the variance of the random output. In problems where the use ...

Quasi-Monte Carlo (QMC) methods have been successfully used to compute high-dimensional integrals arising in many applications, especially in finance. To understand this success and the possible potential limitations of QMC, this paper focuses on quantitative measures of the quality of a point set in high dimensions. We introduce the order-`, superposition and truncation discrepancies, which me...

The Soból sequence is the most popular quasirandom sequence because of its simplicity and efficiency in implementation. We summarize aspects of the scrambling technique applied to Soból sequences and propose a new simpler modified scrambling algorithm, called the multi-digit scrambling scheme. Most proposed scrambling methods randomize a single digit at each iteration. In contrast, our multi-di...

We introduce a new method for screening inputs in mathematical or computational models with large numbers of inputs. The method proposed here represents an improvement over the best available practice for this setting when dealing with models having strong interaction effects. When the sample size is sufficiently high the same design can also be used to obtain accurate quantitative estimates of...

We introduce a class of functions in d ≥ 3 dimensions which have arbitrary odd superposition effective dimensions between three and d inclusive. We prove that for the integration of any function in this class any Sobol’ points of a fixed length have zero error, whereas Owen’s scrambling of any Sobol’ points of the same length has the same variance of error as simple Monte Carlo methods. Further...