An optimal tradeoff between explorations and repetitions in global sensitivity analysis for stochastic computer models

Gildas Mazo (1, 2, 3)

1 MaIAGE - Mathématiques et Informatique Appliquées du Génome à l'Environnement [Jouy-En-Josas]
2 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques
3 Université Paris Saclay (COmUE)

Global 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 methods, permit to quantify the contribution of the inputs to the variability of the output. However, stochastic computer models raise difficulties. There is no unique definition of Sobol indices and their estimation is difficult because a good balance between repetitions of the computer code and explorations of the input space must be found. The problem of finding an optimal tradeoff between explorations and repetitions is addressed. Two kinds of Sobol-like indices are considered. Their estimators are built and their asymptotic properties are established. To find an optimal tradeoff between repetitions and explorations, an error criterion that penalizes bad rankings of the inputs is considered. A bound is found and minimized under a fixed computing budget. Estimators that asymptotically achieve the minimal bound are built. Numerical tests are performed.

Mots clés: stochas- tic; estimation; repetitions; model; random; Sobol; stochastic; Explorations; efficient; sensitivity; model 16 AMS subject classifications 62G20; 60H99; 65C05 17

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

Gildas Mazo. An optimal tradeoff between explorations and repetitions in global sensitivity analysis for stochastic computer models. 2020. ⟨hal-02113448v3⟩