The Annals of Applied Probability

On convergence rates of Gibbs samplers for uniform distributions

Gareth O. Roberts and Jeffrey S. Rosenthal

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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.

Article information

Ann. Appl. Probab., Volume 8, Number 4 (1998), 1291-1302.

First available in Project Euclid: 9 August 2002

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Zentralblatt MATH identifier

Primary: 60J05: Discrete-time Markov processes on general state spaces
Secondary: 62M05: Markov processes: estimation

Gibbs sampler Markov chain Monte Carlo slice sampler uniform distribution curvature


Roberts, Gareth O.; Rosenthal, Jeffrey S. On convergence rates of Gibbs samplers for uniform distributions. Ann. Appl. Probab. 8 (1998), no. 4, 1291--1302. doi:10.1214/aoap/1028903381.

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