Statistical inference for Sobol pick freeze Monte Carlo method

Fabrice Gamboa (1) , Alexandre Janon (2, 3, 4) , Thierry Klein (1) , Agnes Lagnoux-Renaudie (1) , Clémentine Prieur (2, 4)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques
3 SAF - Laboratoire de Sciences Actuarielle et Financière
4 AIRSEA - Mathematics and computing applied to oceanic and atmospheric flows

Many mathematical models involve input parameters, which are not precisely known. Global sensitivity analysis aims to identify the parameters whose uncertainty has the largest impact on the variability of a quantity of interest (output of the model). One of the statistical tools used to quantify the influence of each input variable on the output is the Sobol sensitivity index. We consider the statistical estimation of this index from a finite sample of model outputs. We study asymptotic and non-asymptotic properties of two estimators of Sobol indices. These properties are applied to significance tests and estimation by confidence intervals.

Domaines: Applications [stat.AP]; Méthodologie [stat.ME]; Théorie [stat.TH]; Statistiques [math.ST]

Fabrice Gamboa, Alexandre Janon, Thierry Klein, Agnes Lagnoux-Renaudie, Clémentine Prieur. Statistical inference for Sobol pick freeze Monte Carlo method. Statistics, 2016, 50 (4), pp.881-902. ⟨10.1080/02331888.2015.1105803⟩. ⟨hal-00804668⟩