Articlegreen2015

Statistical inference for Sobol pick-freeze Monte Carlo method

Fabrice Gamboa · Alexandre Janon · Thierry Klein · Agnès Lagnoux · Clémentine Prieur

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

Abstract

Many mathematical models involve input parameters, which are not precisely known. Global sensitivity analysis aims to identify the parameters whose uncertainty has the largest impact on the variability of a quantity of interest (output of the model). One of the statistical tools used to quantify the influence of each input variable on the output is the Sobol sensitivity index. We consider the statistical estimation of this index from a finite sample of model outputs. We study asymptotic and non-asymptotic properties of two estimators of Sobol indices. These properties are applied to significance tests and estimation by confidence intervals.

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References

2001Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates 1996Importance measures in global sensitivity analysis of nonlinear models 2006Survey of sampling-based methods for uncertainty and sensitivity analysis 2002An importance quantification technique in uncertainty analysis for computer models 2013Asymptotic normality and efficiency of two Sobol index estimators 2008Uncertainty in Industrial Practice 2013Better estimation of small sobol' sensitivity indices 2013Variance Components and Generalized Sobol' Indices

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