Sensitivity analysis based on Cramér von Mises distance

Fabrice Gamboa (1) , Thierry Klein (1) , Agnès Lagnoux (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

In this paper, we first study a new sensitivity index that is based on higher moments and generalizes the so-called Sobol one. Further, following an idea of Borgonovo ([3]), we define and study a new sensitivity index based on the Cramér von Mises distance. This new index appears to be more general than the Sobol one as it takes into account, not only the variance, but the whole distribution of the random variable. Furthermore, we study the statistical properties of a Monte Carlo estimate of this new index.

Mots clés: Sensitivity analysis; Cramér von Mises distance; Pick and Freeze method; functional delta-method; Anderson-Darling statistic

Domaines: Probabilités [math.PR]; Statistiques [math.ST]

Fabrice Gamboa, Thierry Klein, Agnès Lagnoux. Sensitivity analysis based on Cramér von Mises distance. 2015. ⟨hal-01163393v1⟩