Articlegreen2013

Variance Components and Generalized Sobol' Indices

102 citations0/0 files storedSIAM/ASA Journal on Uncertainty Quantification

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Probabilistic and Robust Engineering Design Mathematical Approximation and Integration Gaussian Processes and Bayesian Inference

Abstract

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 [Comput. Phys. Comm., 145 (2002), pp. 280--297] and Mauntz [Global Sensitivity Analysis of General Nonlinear Systems, Master's thesis, Imperial College, London, 2002] as well as some new estimators for specific variance components and mean dimensions. This paper also provides a bias corrected version of the estimator of Janon et al. [Asymptotic Normality and Efficiency of Two Sobol' Index Estimators, technical report, INRIA, Rocquencourt, France] and extends the bias correction to generalized Sobol' indices. Some numerical comparisons are given.

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References

2007Global Sensitivity Analysis. The Primer 2001Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates 1978Statistics for experimenters. An introduction to design, data analysis, and model building.2002Making best use of model evaluations to compute sensitivity indices 2004Probabilistic Sensitivity Analysis of Complex Models: A Bayesian Approach 2006Estimating the approximation error when fixing unessential factors in global sensitivity analysis

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2016Global sensitivity analysis using low-rank tensor approximations 2015Statistical inference for Sobol pick-freeze Monte Carlo method 2013Transformations and Invariance in the Sensitivity Analysis of Computer Experiments 2018Multifidelity Monte Carlo Estimation of Variance and Sensitivity Indices 2018Sensitivity Analysis Based on Cramér--von Mises Distance 2014A randomized orthogonal array-based procedure for the estimation of first- and second-order Sobol' indices 2015Introduction to Sensitivity Analysis

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