Calculations of Sobol indices for the Gaussian process metamodel

Amandine Marrel (1, 2, 3) , Bertrand Iooss (3, 4) , Béatrice Laurent (5) , Olivier Roustant (6)

1 LMTE - Laboratoire de Modélisation des Transferts dans l'Environnement
2 CEA - Commissariat à l'énergie atomique et aux énergies alternatives
3 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques
4 LCFR - Laboratoire de Conduite et Fiabilité des Réacteurs
5 IMT - Institut de Mathématiques de Toulouse UMR5219
6 3MI-ENSMSE - Département Méthodes et Modèles Mathématiques pour l'Industrie

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.

Mots clés: sensitivity analysis; uncertainty; computer code; Gaussian process; covariance; metamodel

Domaines: Méthodologie [stat.ME]; Statistiques [math.ST]; Théorie [stat.TH]

Amandine Marrel, Bertrand Iooss, Béatrice Laurent, Olivier Roustant. Calculations of Sobol indices for the Gaussian process metamodel. Reliability Engineering and System Safety, 2009, 94, pp.742-751. ⟨10.1016/j.ress.2008.07.008⟩. ⟨hal-00239494⟩