The Sobol method in sensitivity analysis for stochastic computer models

Gildas Mazo (1)

1 MaIAGE - Mathématiques et Informatique Appliquées du Génome à l'Environnement [Jouy-En-Josas]

Sensitivity analysis often accompanies computer modeling to understand what are the important factors of a model of interest. In particular , Sobol indices, naturally estimated by Monte-Carlo sampling, permit to quantify the contribution of the inputs to the variability of the output. However, when the model is stochastic, the problem of carrying out a sensitivity analysis remains open. There is no unique definition of Sobol indices and their estimation is more difficult because a good balance between repetitions of the computer code and explorations of the input space must be found. The problem of performing a sensitivity analysis for stochastic computer models with the Sobol method is addressed. Two Sobol indices are considered, their estimators constructed and their asymptotic properties established. An optimal balance between repetitions and explorations is proposed under a limited computing budget. A two-stage procedure is built: the first stage permits to find the optimal balance and the second stage produces the Sobol estimates based on the balance obtained in the first stage. The procedure is asymptotically oracle and the optimal convergence rates are derived. The theoretical results are tested with numerical experiments.

Mots clés: Sobol; sensitivity; stochastic; random; model; efficient

Domaines: Théorie [stat.TH]; Calcul [stat.CO]; Modélisation et simulation

Gildas Mazo. The Sobol method in sensitivity analysis for stochastic computer models. 2019. ⟨hal-02113448v1⟩