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arXiv · 2605.30979

On weighted Poincar{\'e} inequalities for multivariate Liouville distributions -- Application to Global Sensitivity Analysis

David Heredia
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Abstract

In this work we establish weighted Poincar{\'e} 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 Poincar{\'e} 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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David Heredia. 2026-05-29. On weighted Poincar{\'e} inequalities for multivariate Liouville distributions -- Application to Global Sensitivity Analysis. https://arxiv.org/abs/2605.30979

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