Functional inequalities for perturbed measures with applications to log-concave measures and to some Bayesian problems
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Publication:6359151
DOI10.3150/21-BEJ1419arXiv2101.11257MaRDI QIDQ6359151
Publication date: 27 January 2021
Abstract: We study functional inequalities (Poincar'e, Cheeger, log-Sobolev) for probability measures obtained as perturbations. Several explicit results for general measures as well as log-concave distributions are given.The initial goal of this work was to obtain explicit bounds on the constants in view of statistical applications for instance. These results are then applied to the Langevin Monte-Carlo method used in statistics in order to compute Bayesian estimators.
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