Open Access
VOL. 10 | 2013 On the Geometric Ergodicity of Two-Variable Gibbs Samplers
Aixin Tan, Galin L. Jones, James P. Hobert

Editor(s) Galin Jones, Xiaotong Shen

Inst. Math. Stat. (IMS) Collect., 2013: 25-42 (2013) DOI: 10.1214/12-IMSCOLL1002


A Markov chain is geometrically ergodic if it converges to its invariant distribution at a geometric rate in total variation norm. We study geometric ergodicity of deterministic and random scan versions of the two-variable Gibbs sampler. We give a sufficient condition which simultaneously guarantees both versions are geometrically ergodic. We also develop a method for simultaneously establishing that both versions are subgeometrically ergodic. These general results allow us to characterize the convergence rate of two-variable Gibbs samplers in a particular family of discrete bivariate distributions.


Published: 1 January 2013
First available in Project Euclid: 23 September 2013

zbMATH: 1329.60257
MathSciNet: MR3586937

Digital Object Identifier: 10.1214/12-IMSCOLL1002

Primary: 60J10
Secondary: 62F15

Keywords: geometric ergodicity , Gibbs sampler , Markov chain , Monte Carlo

Rights: Copyright © 2013, Institute of Mathematical Statistics

Back to Top