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

¹ Institut de Recherche en Mathématique Avancée, Université de Strasbourg, France.
² Université Paris Sud (Paris Saclay), Laboratoire de Mathématiques d’Orsay, CNRS UMR 8628, France.
³ Université de Lyon, Université Lyon 1, Institut Camille Jordan ICJ UMR 5208 CNRS, France.
⁴ Université de Lyon, Université Lyon 1, Laboratoire SAF EA 2429, France.

^* Corresponding author: alexandre.janon@math.u-psud.fr

Received: 22 January 2017
Accepted: 3 January 2018

Abstract

In the past decade, Sobol’s variance decomposition has been used as a tool to assess how the output of a model is affected by the uncertainty on its input parameters. We show some links between global sensitivity analysis and stochastic ordering theory. More specifically, we study the influence of inputs’ distributions on Sobol indices in relation with stochastic orders. This gives an argument in favor of using Sobol’s indices in uncertainty quantification, as one indicator among others.