Global sensitivity analysis of stochastic computer models with joint metamodels

Bertrand Iooss (1, 2) , Mathieu Ribatet (3) , Amandine Marrel (4)

1 LCFR - Laboratoire de Conduite et Fiabilité des Réacteurs
2 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques
3 UM - Université de Montpellier
4 LMTE - Laboratoire de Modélisation des Transferts dans l'Environnement

The global sensitivity analysis method, used to quantify the influence of uncertain input variables on the response variability of a numerical model, is applicable to deterministic computer code (for which the same set of input variables gives always the same output value). This paper proposes a global sensitivity analysis methodology for stochastic computer code (having a variability induced by some uncontrollable variables). The framework of the joint modeling of the mean and dispersion of heteroscedastic data is used. To deal with the complexity of computer experiment outputs, non parametric joint models (based on Generalized Additive Models and Gaussian processes) are discussed. The relevance of these new models is analyzed in terms of the obtained variance-based sensitivity indices with two case studies. Results show that the joint modeling approach leads accurate sensitivity index estimations even when clear heteroscedasticity is present.

Mots clés: Computer experiment · Generalized additive model · Gaussian process · Joint modeling · Sobol indices · Uncertainty

Domaines: Méthodologie [stat.ME]; Applications [stat.AP]

Bertrand Iooss, Mathieu Ribatet, Amandine Marrel. Global sensitivity analysis of stochastic computer models with joint metamodels. 2009. ⟨hal-00232805v3⟩