{"ID":2900892,"CreatedAt":"2026-06-01T05:51:17.9442275Z","UpdatedAt":"2026-06-01T06:23:29.641557848Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2605.30979","arxiv_id":"2605.30979","title":"On weighted Poincar{é} inequalities for multivariate Liouville distributions -- Application to Global Sensitivity Analysis","abstract":"In this work we establish weighted Poincar{é} 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{é} 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.","short_abstract":"In this work we establish weighted Poincar{é} 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 argume...","url_abs":"https://arxiv.org/abs/2605.30979","url_pdf":"https://arxiv.org/pdf/2605.30979v1","authors":"[\"David Heredia\"]","published":"2026-05-29T08:17:50Z","proceeding":"math.FA","tasks":"[\"math.FA\",\"math.PR\",\"math.ST\"]","methods":"[]","has_code":false}