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June 3, 20260 citationsOpen Access

On weighted Poincaré inequalities for multivariate Liouville distributions -- Application to Global Sensitivity Analysis

DHDavid HerediaCentre National de la Recherche Scientifique

Key Points

This work aims to establish weighted Poincaré inequalities for multivariate Liouville distributions and apply them to global sensitivity analysis.
Investigated multivariate Liouville distributions and continuous elliptically contoured distributions.
Utilized a transport argument to transfer weights between probability measures.
Applied findings to a flood model using classical copulas to encode variable dependence.
Demonstrated the effective application of weighted Poincaré inequalities in modeling multivariate distributions.
Illustrated enhanced sensitivity analysis outcomes in the flood model case study through improved dependence structure.

Abstract

In this work we establish weighted Poincaré inequalities for multivariate Liouville distributions, which are a generalization of the Dirichlet distribution. We also consider continuous elliptically contoured distributions, whose density levels are unions of hyperellipsoids. Our approach is based on a transport argument which allows weighted Poincaré inequalities to be transferred between probability measures. We apply our results to global sensitivity analysis and illustrate their practical use in a flood model case study, where the structure of dependence of the input variables is encoded by classical copulas.

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