On the consistency of Sobol indices with respect to stochastic ordering of model parameters.

Areski Cousin (1, 2) , Alexandre Janon (3, 4) , Véronique Maume-Deschamps (5, 6) , Ibrahima Niang (1)

1 SAF - Laboratoire de Sciences Actuarielle et Financière
2 IRMA - Institut de Recherche Mathématique Avancée
3 LM-Orsay - Laboratoire de Mathématiques d'Orsay
4 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques
5 ICJ - Institut Camille Jordan
6 PSPM - Probabilités, statistique, physique mathématique

In the past decade, Sobol's variance decomposition have been used as a tool - among others - in risk management. We show some links between global sensitivity analysis and stochastic ordering theories. This gives an argument in favor of using Sobol's indices in uncertainty quantification, as one indicator among others.

Keywords: global sensibility analysis; Sobol index; excess wealth order; dispersive order; stochastic orders

Domains: Statistics [math.ST]; Statistics Theory [stat.TH]; Probability [math.PR]

Areski Cousin, Alexandre Janon, Véronique Maume-Deschamps, Ibrahima Niang. On the consistency of Sobol indices with respect to stochastic ordering of model parameters.. ESAIM: Probability and Statistics, 2019, 23 (387-408), ⟨10.1051/ps/2018001⟩. ⟨hal-01026373v2⟩