Sensitivity analysis based on Cram{\'e}r von Mises distance

TL;DR

This paper introduces a new sensitivity index based on the Cramér von Mises distance that considers the entire distribution of a random variable, extending traditional variance-based methods like Sobol indices.

Contribution

It proposes a novel sensitivity index using the Cramér von Mises distance and analyzes its statistical properties, broadening the scope of sensitivity analysis beyond variance.

Findings

The new index generalizes Sobol indices by incorporating full distribution information.

Statistical properties of Monte Carlo estimates for the new index are studied.

The approach offers a more comprehensive sensitivity analysis method.

Abstract

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 Cram{\'e}r 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.