May 2022 Convergence rates of two-component MCMC samplers
Qian Qin, Galin L. Jones
Author Affiliations +
Bernoulli 28(2): 859-885 (May 2022). DOI: 10.3150/21-BEJ1369


Component-wise MCMC algorithms, including Gibbs and conditional Metropolis-Hastings samplers, are commonly used for sampling from multivariate probability distributions. A long-standing question regarding Gibbs algorithms is whether a deterministic-scan (systematic-scan) sampler converges faster than its random-scan counterpart. We answer this question when the samplers involve two components by establishing an exact quantitative relationship between the L2 convergence rates of the two samplers. The relationship shows that the deterministic-scan sampler converges faster. We also establish qualitative relations among the convergence rates of two-component Gibbs samplers and some conditional Metropolis-Hastings variants. For instance, it is shown that if some two-component conditional Metropolis-Hastings samplers are geometrically ergodic, then so are the associated Gibbs samplers.

Funding Statement

The first author was partially supported by the National Science Foundation. The second author was partially supported by the National Science Foundation.


We thank the Editor, the Associate Editor, and two anonymous reviewers for their constructive feedback.


Download Citation

Qian Qin. Galin L. Jones. "Convergence rates of two-component MCMC samplers." Bernoulli 28 (2) 859 - 885, May 2022.


Received: 1 June 2020; Revised: 1 January 2021; Published: May 2022
First available in Project Euclid: 3 March 2022

MathSciNet: MR4388922
zbMATH: 07526568
Digital Object Identifier: 10.3150/21-BEJ1369

Keywords: Deterministic-scan , geometric ergodicity , Gibbs , Metropolis-within-Gibbs , random-scan

Rights: Copyright © 2022 ISI/BS


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Vol.28 • No. 2 • May 2022
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