# Robustness of the Sobol' indices to marginal distribution uncertainty

## TL;DR

This paper introduces a new method to assess how sensitive Sobol' indices are to uncertainties in the marginal probability distributions of input variables in global sensitivity analysis, enhancing the robustness evaluation.

## Contribution

It proposes a novel approach using optimal perturbations of marginal distributions to analyze Sobol' indices' robustness under distributional uncertainty.

## Key findings

- Method effectively quantifies robustness of Sobol' indices
- Illustrated with synthetic examples and a contaminant transport model
- Provides insights into distributional assumptions impact on sensitivity analysis

## Abstract

Global sensitivity analysis (GSA) quantifies the influence of uncertain variables in a mathematical model. The Sobol' indices, a commonly used tool in GSA, seek to do this by attributing to each variable its relative contribution to the variance of the model output. In order to compute Sobol' indices, the user must specify a probability distribution for the uncertain variables. This distribution is typically unknown and must be chosen using limited data and/or knowledge. The usefulness of the Sobol' indices depends on their robustness to this distributional uncertainty. This article presents a novel method which uses "optimal perturbations" of the marginal probability density functions to analyze the robustness of the Sobol' indices. The method is illustrated through synthetic examples and a model for contaminant transport.