The Annals of Applied Probability

On convergence rates of Gibbs samplers for uniform distributions

Gareth O. Roberts and Jeffrey S. Rosenthal

Full-text: Open access

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.

Article information

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

Dates
First available in Project Euclid: 9 August 2002

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1028903381

Digital Object Identifier
doi:10.1214/aoap/1028903381

Mathematical Reviews number (MathSciNet)
MR1661176

Zentralblatt MATH identifier
0935.60054

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

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

Citation

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. https://projecteuclid.org/euclid.aoap/1028903381


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