Global Sensitivity Analysis: a new generation of mighty estimators based on rank statistics

Understand

We propose a new statistical estimation framework for a large family of global sensitivity analysis methods.

• Our approach is based on rank statistics and uses an empirical correlation coefficient recently introduced by Sourav Chatterjee.
• We show how to apply this approach to compute not only the Cram\'er-von-Mises indices, which are directly related to Chatterjee's notion of correlation, but also Sobol indices at any order, higher-order moment indices, and Shapley effects.
• We establish consistency of the resulting estimators and demonstrate their numerical efficiency, especially for small sample sizes.