Sensitivity Analysis and Generalized Chaos Expansions. Lower Bounds for Sobol indices
Statistics Theory
2019-06-25 v1 Statistics Theory
Abstract
The so-called polynomial chaos expansion is widely used in computer experiments. For example, it is a powerful tool to estimate Sobol' sensitivity indices. In this paper, we consider generalized chaos expansions built on general tensor Hilbert basis. In this frame, we revisit the computation of the Sobol' indices and give general lower bounds for these indices. The case of the eigenfunctions system associated with a Poincar{\'e} differential operator leads to lower bounds involving the derivatives of the analyzed function and provides an efficient tool for variable screening. These lower bounds are put in action both on toy and real life models demonstrating their accuracy.
Keywords
Cite
@article{arxiv.1906.09883,
title = {Sensitivity Analysis and Generalized Chaos Expansions. Lower Bounds for Sobol indices},
author = {O Roustant and F. Gamboa and B Iooss},
journal= {arXiv preprint arXiv:1906.09883},
year = {2019}
}