Robustness of the Sobol' indices to distributional uncertainty

TL;DR

This paper investigates how sensitive Sobol' indices are to uncertainties in the probability distributions of variables in global sensitivity analysis, proposing a minimal-knowledge robustness assessment method.

Contribution

It introduces a new method to evaluate the robustness of Sobol' indices against distributional uncertainties with minimal user input and no extra model evaluations.

Findings

The method effectively assesses Sobol' indices robustness.

Theoretical and computational analyses validate the approach.

Illustrative examples demonstrate practical applicability.

Abstract

Global sensitivity analysis (GSA) is used to quantify the influence of uncertain variables in a mathematical model. Prior to performing GSA, the user must specify (or implicitly assume), a probability distribution to model the uncertainty, and possibly statistical dependencies, of the variables. Determining this distribution is challenging in practice as the user has limited and imprecise knowledge of the uncertain variables. This article analyzes the robustness of the Sobol' indices, a commonly used tool in GSA, to changes in the distribution of the uncertain variables. A method for assessing such robustness is developed which requires minimal user specification and no additional evaluations of the model. Theoretical and computational aspects of the method are considered and illustrated through examples.