Calculations of Sobol indices for the Gaussian process metamodel Export

@article{citeulike:5984224, abstract = {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.}, author = {Marrel, A. and Iooss, B. and Laurent, B. and Roustant, O.}, citeulike-article-id = {5984224}, citeulike-linkout-0 = {http://dx.doi.org/10.1016/j.ress.2008.07.008}, citeulike-linkout-1 = {http://linkinghub.elsevier.com/retrieve/pii/S0951832008001981}, doi = {10.1016/j.ress.2008.07.008}, issn = {09518320}, journal = {Reliability Engineering \& System Safety}, keywords = {analytic, kriging, metamodel, sensitivity\_analysis, uncertainty}, month = {March}, number = {3}, pages = {742--751}, posted-at = {2009-10-22 09:45:52}, priority = {2}, title = {Calculations of Sobol indices for the Gaussian process metamodel}, url = {http://dx.doi.org/10.1016/j.ress.2008.07.008}, volume = {94}, year = {2009} }

TY - JOUR ID - citeulike:5984224 L3 - citeulike-article-id:5984224 N2 - 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. IS - 3 JF - Reliability Engineering & System Safety SN - 09518320 EP - 751 TI - Calculations of Sobol indices for the Gaussian process metamodel VL - 94 SP - 742 KW - analytic KW - kriging KW - metamodel KW - sensitivity_analysis KW - uncertainty AU - Marrel, A AU - Iooss, B AU - Laurent, B AU - Roustant, O PY - 2009/03// UR - http://dx.doi.org/10.1016/j.ress.2008.07.008 ER -