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

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

1 SAF - Laboratoire de Sciences Actuarielle et Financière
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay
3 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques
4 ICJ - Institut Camille Jordan

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.

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

Domaines: Statistiques [math.ST]; Théorie [stat.TH]; Probabilités [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.. 2014. ⟨hal-01026373v1⟩