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On the geometric ergodicity of two-variable Gibbs samplers. (English) Zbl 1329.60257

Jones, Galin (ed.) et al., Advances in modern statistical theory and applications. A Festschrift in honor of Morris L. Eaton. Beachwood, OH: IMS, Institute of Mathematical Statistics (ISBN 978-0-940600-84-3). Institute of Mathematical Statistics Collections 10, 25-42 (2013).
Summary: 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 that 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.
For the entire collection see [Zbl 1319.62004].

MSC:

60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
62F15 Bayesian inference
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