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November 1998 On convergence rates of Gibbs samplers for uniform distributions
Gareth O. Roberts, Jeffrey S. Rosenthal
Ann. Appl. Probab. 8(4): 1291-1302 (November 1998). DOI: 10.1214/aoap/1028903381

Abstract

We consider a Gibbs sampler applied to the uniform distribution on a bounded region $R \subseteq \mathbf{R}^d$. We show that the convergence properties of the Gibbs sampler depend greatly on the smoothness of the boundary of R. Indeed, for sufficiently smooth boundaries the sampler is uniformly ergodic, while for jagged boundaries the sampler could fail to even be geometrically ergodic.

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Gareth O. Roberts. Jeffrey S. Rosenthal. "On convergence rates of Gibbs samplers for uniform distributions." Ann. Appl. Probab. 8 (4) 1291 - 1302, November 1998. https://doi.org/10.1214/aoap/1028903381

Information

Published: November 1998
First available in Project Euclid: 9 August 2002

zbMATH: 0935.60054
MathSciNet: MR1661176
Digital Object Identifier: 10.1214/aoap/1028903381

Subjects:
Primary: 60J05
Secondary: 62M05

Keywords: curvature , Gibbs sampler , Markov chain , Monte Carlo , slice sampler , uniform distribution

Rights: Copyright © 1998 Institute of Mathematical Statistics

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Vol.8 • No. 4 • November 1998
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