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.
David Heredia (Fri,) studied this question.