Functional inequalities for perturbed measures with applications to log-concave measures and to some Bayesian problems
Probability
2021-01-28 v1 Statistics Theory
Statistics Theory
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.
Cite
@article{arxiv.2101.11257,
title = {Functional inequalities for perturbed measures with applications to log-concave measures and to some Bayesian problems},
author = {Patrick Cattiaux and Arnaud Guillin},
journal= {arXiv preprint arXiv:2101.11257},
year = {2021}
}