On the consistency of Sobol indices with respect to stochastic ordering of model parameters

TL;DR

This paper explores the relationship between Sobol indices and stochastic ordering, providing theoretical insights that support the use of Sobol's variance-based sensitivity measures in risk management and uncertainty quantification.

Contribution

It establishes links between global sensitivity analysis and stochastic ordering theories, enhancing the theoretical foundation for using Sobol indices in uncertainty quantification.

Findings

Sobol indices are consistent with stochastic ordering principles.

Theoretical support for Sobol's indices in risk management.

Enhanced understanding of sensitivity measures in probabilistic models.

Abstract

In the past decade, Sobol's variance decomposition have been used as a tool - among others - in risk management. We show some links between global sensitivity analysis and stochastic ordering theories. This gives an argument in favor of using Sobol's indices in uncertainty quantification, as one indicator among others.