Sensitivity analysis in general metric spaces

Sensitivity indices are commonly used to quantity the relative influence of any specific group of input variables on the output of a computer code. In this paper, we introduce new sensitivity indices adapted to outputs valued in general metric spaces. This new class of indices encompasses the classical ones; in particular, the so-called Sobol indices and the Cramer-von-Mises indices. Furthermore, we provide asymptotically Gaussian estimators of these indices based on U-statistics. Surprisingly, we prove the asymptotic normality straightforwardly. Finally, we illustrate this new procedure on a toy model and on two real-data examples.

Automated summary

This paper introduces new sensitivity indices adapted to outputs valued in general metric spaces, encompassing classical ones such as Sobol indices and Cramer-von-Mises indices. Asymptotically Gaussian estimators of these indices based on U-statistics are provided, with surprising straightforward proof of asymptotic normality. The new procedure is illustrated on a toy model and two real-data examples.