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.
Estimation and model errors in Gaussian-process-based Sensitivity Analysis of functional outputs
Institut de Mathématiques de Toulouse, Université de Toulouse（图卢兹数学研究所，图卢兹大学）；São Paulo State University “Júlio de Mesquita Filho” (UNESP)（圣保罗州立大学（朱利奥·德·梅斯基塔·菲略））
Learning Global Sensitivity Indices from Observational Data: A Metamodel-Based Approach
University of Naples Federico II（那不勒斯费德里科二世大学）；Polytechnic and Basic Sciences School（理工与基础科学学院）；Department of Electrical Engineering and Information Technology（电气与信息工程系）
