Calculations of Sobol indices for the Gaussian process metamodel

By Amandine Marrel, Bertrand Iooss, Béatrice Laurent, O. Roustant. Reliability Engineering & System Safety, 2008

371 citations recorded by the source corpus.

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 metamodel, predicting the model responses with a negligible computation time and rending straightforward the estimation of Sobol indices. In this paper, we discuss about the Gaussian process model which gives analytical expressions of Sobol indices. Two approaches are studied to compute the Sobol indices: the first based on the predictor of the Gaussian process model and the second based on the global stochastic process model. Comparisons between the two estimates, made on analytical examples, show the superiority of the second approach in terms of convergence and robustness. Moreover, the second approach allows to integrate the modeling error of the Gaussian process model by directly giving some confidence intervals on the Sobol indices. These techniques are finally applied to a real case of hydrogeological modeling.

Subfields: Environmental Engineering, Ocean Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/95c65aeb15d56453374dc74df625f8eb8e55c1f8

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Citations in the corpus

Use of global sensitivity analysis and polynomial chaos expansion for interpretation of nonreactive transport experiments in laboratory‐scale porous media (2011, background): “…experiments in system biology [e.g., Kontoravdi et al., 2005; van Riel, 2006; Kiparissides et al., 2009, and references therein], reliability engineering [e.g., Frey and Patil, 2002; Marrel et al., 2009], and within practices of risk assessment of groundwater pollution [e.g., Volkova et al., 2008].”
ANOVA kernels and RKHS of zero mean functions for model-based sensitivity analysis (2011, positive): “Following [12], it can then be advantageous to perform the sensitivity analysis on a surrogate model m approximating f .”
New improvements in the use of dependence measures for sensitivity analysis and screening (2014, background): “[18] and Sudret [19] estimate the Sobol’ indices thanks to Gaussian process models and polynomial chaos expansions, respectively.”
Metamodel-based sensitivity analysis: polynomial chaos expansions and Gaussian processes (2016, positive): “For more detail about this approach, the reader is referred to Oakley and O’Hagan [42]; Marrel et al. [37].”
Asymptotic normality and efficiency of two Sobol index estimators (2013, positive): “Some work has been done on the non-asymptotic error quantiﬁcation in Sobol index estimation in earlier papers [13, 16, 29] by means of conﬁdence intervals which account for both sampling and metamodel errors.”
The Future of Sensitivity Analysis: An essential discipline for systems modeling and policy support (2020, positive): “Once built, sensitivity measures can be estimated by sampling the surrogate instead of the original model at negligible cost, or, in some cases, can be estimated analytically (Sudret, 2008; Marrel et al., 2009).”