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April 2021 Quantitative spectral gap estimate and Wasserstein contraction of simple slice sampling
Viacheslav Natarovskii, Daniel Rudolf, Björn Sprungk
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Ann. Appl. Probab. 31(2): 806-825 (April 2021). DOI: 10.1214/20-AAP1605

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.

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Viacheslav Natarovskii. Daniel Rudolf. Björn Sprungk. "Quantitative spectral gap estimate and Wasserstein contraction of simple slice sampling." Ann. Appl. Probab. 31 (2) 806 - 825, April 2021. https://doi.org/10.1214/20-AAP1605

Information

Received: 1 March 2019; Revised: 1 March 2020; Published: April 2021
First available in Project Euclid: 1 April 2021

Digital Object Identifier: 10.1214/20-AAP1605

Subjects:
Primary: 65C40
Secondary: 60J22, 62D99, 65C05

Rights: Copyright © 2021 Institute of Mathematical Statistics

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Vol.31 • No. 2 • April 2021
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