On convergence rates of Gibbs samplers for uniform distributions

Citation
Go. Roberts et Js. Rosenthal, On convergence rates of Gibbs samplers for uniform distributions, ANN APPL PR, 8(4), 1998, pp. 1291-1302
Citations number
14
Categorie Soggetti
Mathematics
Journal title
ANNALS OF APPLIED PROBABILITY
ISSN journal
10505164 → ACNP
Volume
8
Issue
4
Year of publication
1998
Pages
1291 - 1302
Database
ISI
SICI code
1050-5164(199811)8:4<1291:OCROGS>2.0.ZU;2-V
Abstract
We consider a Gibbs sampler applied to the uniform distribution on a bounde d region R subset of or equal to R-d. We show that the convergence properti es of the Gibbs sampler depend greatly on the smoothness of the boundary of R. Indeed, for sufficiently smooth boundaries the sampler is uniformly erg odic, while for jagged boundaries the sampler could fail to even be geometr ically ergodic.