A Bayesian approach for global sensitivity analysis of (multi-fidelity) computer codes

Loic Le Gratiet (1, 2) , Claire Cannamela (2) , Bertrand Iooss (2, 3)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques
3 EDF R&D MRI - Management des Risques Industriels

Complex computer codes are widely used in science and engineering to model physical phenomena. Furthermore, it is common that they have a large number of input parameters. Global sensitivity analysis aims to identify those which have the most important impact on the output. Sobol indices are a popular tool to perform such analysis. However, their estimations require an important number of simulations and often cannot be processed under reasonable time constraint. To handle this problem, a Gaussian process regression model is built to surrogate the computer code and the Sobol indices are estimated through it. The aim of this paper is to provide a methodology to estimate the Sobol indices through a surrogate model taking into account both the estimation errors and the surrogate model errors. In particular, it allows us to derive non-asymptotic confidence intervals for the Sobol index estimations. Furthermore, we extend the suggested strategy to the case of multi-fidelity computer codes which can be run at different levels of accuracy. For such simulators, we use an extension of Gaussian process regression models for multivariate outputs.

Mots clés: Sensitivity analysis; Gaussian process regression; multi-fidelity model; complex computer codes; Sobol index; Bayesian analysis

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

Loic Le Gratiet, Claire Cannamela, Bertrand Iooss. A Bayesian approach for global sensitivity analysis of (multi-fidelity) computer codes. SIAM/ASA Journal on Uncertainty Quantification, 2014, 2, pp.336-363. ⟨hal-00842432⟩