# Sensitivity Analysis and Generalized Chaos Expansions. Lower Bounds for Sobol indices

## TL;DR

This paper introduces generalized chaos expansions based on tensor Hilbert bases to estimate Sobol' sensitivity indices, providing new lower bounds that enhance variable screening in complex models.

## Contribution

It develops a generalized framework for chaos expansions and derives lower bounds for Sobol' indices, improving sensitivity analysis methods.

## Key findings

- Lower bounds for Sobol' indices are established.
- Bounds are effective for variable screening.
- Demonstrated accuracy on toy and real models.

## 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.