GRiLS is a gradient-free MCMC proposal derived via a Lamperti transform of Riemannian Langevin dynamics, using a Gaussian approximation of the target to enable mode-hopping without gradient evaluations.
On weighted Poincar{\'e} inequalities for multivariate Liouville distributions -- Application to Global Sensitivity Analysis
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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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2026 1verdicts
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Gradient-free Riemannian Langevin Sampler
GRiLS is a gradient-free MCMC proposal derived via a Lamperti transform of Riemannian Langevin dynamics, using a Gaussian approximation of the target to enable mode-hopping without gradient evaluations.