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

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  • Johnson, Alicia A.
  • Jones, Galin L.

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.

Suggested Citation

  • Johnson, Alicia A. & Jones, Galin L., 2015. "Geometric ergodicity of random scan Gibbs samplers for hierarchical one-way random effects models," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 325-342.
    • Handle: RePEc:eee:jmvana:v:140:y:2015:i:c:p:325-342
    DOI: 10.1016/j.jmva.2015.06.002
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    Cited by:

    1. Abrahamsen, Tavis & Hobert, James P., 2019. "Fast Monte Carlo Markov chains for Bayesian shrinkage models with random effects," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 61-80.
    2. Dai, Ning & Jones, Galin L., 2017. "Multivariate initial sequence estimators in Markov chain Monte Carlo," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 184-199.

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