Quantitative spectral gap estimate and Wasserstein contraction of simple slice sampling
Probability
2020-09-17 v2 Statistics Theory
Statistics Theory
Abstract
We prove Wasserstein contraction of simple slice sampling for approximate sampling w.r.t. distributions with log-concave and rotational invariant Lebesgue densities. This yields, in particular, an explicit quantitative lower bound of the spectral gap of simple slice sampling. Moreover, this lower bound carries over to more general target distributions depending only on the volume of the (super-)level sets of their unnormalized density.
Cite
@article{arxiv.1903.03824,
title = {Quantitative spectral gap estimate and Wasserstein contraction of simple slice sampling},
author = {Viacheslav Natarovskii and Daniel Rudolf and Björn Sprungk},
journal= {arXiv preprint arXiv:1903.03824},
year = {2020}
}
Comments
24 pages, 6 figures, accepted for publication in Ann. Appl. Probab