Geometric ergodicity of random scan Gibbs samplers for hierarchical one-way random effects models

Alicia A. Johnson; Galin L. Jones

doi:10.1016/j.jmva.2015.06.002

Geometric ergodicity of random scan Gibbs samplers for hierarchical one-way random effects models

Alicia A. Johnson, Galin L. Jones

Statistics (Twin Cities)

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

We consider two Bayesian hierarchical one-way random effects models and establish geometric ergodicity of the corresponding random scan Gibbs samplers. Geometric ergodicity, along with a moment condition, guarantees a central limit theorem for sample means and quantiles. In addition, it ensures the consistency of various methods for estimating the variance in the asymptotic normal distribution. Thus our results make available the tools for practitioners to be as confident in inferences based on the observations from the random scan Gibbs sampler as they would be with inferences based on random samples from the posterior.

Original language	English (US)
Pages (from-to)	325-342
Number of pages	18
Journal	Journal of Multivariate Analysis
Volume	140
DOIs	https://doi.org/10.1016/j.jmva.2015.06.002
State	Published - Sep 1 2015

Bibliographical note

Funding Information:
The second author research was supported by the National Science Foundation DMS-13-10096 and the National Institutes for Health NIBIB R01 EB012547 .

Publisher Copyright:
© 2015 Elsevier Inc.

Keywords

Convergence
Geometric ergodicity
Gibbs sampling
Markov chain Monte Carlo
One-way random effects

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title = "Geometric ergodicity of random scan Gibbs samplers for hierarchical one-way random effects models",

abstract = "We consider two Bayesian hierarchical one-way random effects models and establish geometric ergodicity of the corresponding random scan Gibbs samplers. Geometric ergodicity, along with a moment condition, guarantees a central limit theorem for sample means and quantiles. In addition, it ensures the consistency of various methods for estimating the variance in the asymptotic normal distribution. Thus our results make available the tools for practitioners to be as confident in inferences based on the observations from the random scan Gibbs sampler as they would be with inferences based on random samples from the posterior.",

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AU - Jones, Galin L.

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N2 - We consider two Bayesian hierarchical one-way random effects models and establish geometric ergodicity of the corresponding random scan Gibbs samplers. Geometric ergodicity, along with a moment condition, guarantees a central limit theorem for sample means and quantiles. In addition, it ensures the consistency of various methods for estimating the variance in the asymptotic normal distribution. Thus our results make available the tools for practitioners to be as confident in inferences based on the observations from the random scan Gibbs sampler as they would be with inferences based on random samples from the posterior.

AB - We consider two Bayesian hierarchical one-way random effects models and establish geometric ergodicity of the corresponding random scan Gibbs samplers. Geometric ergodicity, along with a moment condition, guarantees a central limit theorem for sample means and quantiles. In addition, it ensures the consistency of various methods for estimating the variance in the asymptotic normal distribution. Thus our results make available the tools for practitioners to be as confident in inferences based on the observations from the random scan Gibbs sampler as they would be with inferences based on random samples from the posterior.

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KW - Markov chain Monte Carlo

KW - One-way random effects

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Geometric ergodicity of random scan Gibbs samplers for hierarchical one-way random effects models

Abstract

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Keywords

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