Global sensitivity analysis of stochastic computer models with generalized additive models

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

1 IFPEN - IFP Energies nouvelles
2 CEA - Commissariat à l'énergie atomique et aux énergies alternatives
3 EDF R&D - EDF R&D
4 UM2 - Université Montpellier 2 - Sciences et Techniques

The global sensitivity analysis method used to quantify the influence of uncertain input variables on the variability in numerical model responses has already been applied to deterministic computer codes; deterministic means here that the same set of input variables always gives the same output value. This paper proposes a global sensitivity analysis methodology for stochastic computer codes, for which the result of each code run is itself random. 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, nonparametric joint models are discussed and a new Gaussian process-based joint model is proposed. The relevance of these models is analyzed based upon two case studies. Results show that the joint modeling approach yields accurate sensitivity index estimators even when heteroscedasticity is strong.

L-analyse de sensibilite globale, utilisee pour quantifier l-influence de parametres d-entree incertains sur la variabilite de la sortie d-un modele numerique, est applicable pour les codes de calcul deterministes (c-est-a-dire pour lesquels un meme jeu de parametres d-entree donne toujours le meme resultat). Ce papier propose une methode d-analyse de sensibilite globale pour les codes de calcul stochastiques (qui ont une variabilite due a des parametres incontrolables). La moyenne et la dispersion des sorties du code sont modelisees par deux Modeles Additifs Generalises (GAM) interdependants. Le modele de la moyenne permet d-obtenir les indices de sensibilite des parametres controlables, alors que le modele de la dispersion permet d-obtenir les indices des parametres incontrolables. L-interet de ce type de modele est montre sur deux cas d-etude.

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

Mots clés: Modelisation jointe; modele lineaire generalise; incertitude; surface de reponse; moyenne et dispersion

Domaines: Physique Nucléaire Expérimentale [nucl-ex]; Physique Nucléaire Théorique [nucl-th]

Amandine Marrel, Bertrand Iooss, Sébastien da Veiga, Mathieu Ribatet. Global sensitivity analysis of stochastic computer models with generalized additive models. Statistics and Computing, 2009, 22 (3), pp.833-847. ⟨10.1007/s11222-011-9274-8⟩. ⟨cea-02355755⟩