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Geometric Ergodicity of Gibbs and Block Gibbs Samplers for a Hierarchical Random Effects Model

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  • Hobert, James P.
  • Geyer, Charles J.

Abstract

We consider fixed scan Gibbs and block Gibbs samplers for a Bayesian hierarchical random effects model with proper conjugate priors. A drift condition given in Meyn and Tweedie (1993, Chapter 15) is used to show that these Markov chains are geometrically ergodic. Showing that a Gibbs sampler is geometrically ergodic is the first step toward establishing central limit theorems, which can be used to approximate the error associated with Monte Carlo estimates of posterior quantities of interest. Thus, our results will be of practical interest to researchers using these Gibbs samplers for Bayesian data analysis.

Suggested Citation

  • Hobert, James P. & Geyer, Charles J., 1998. "Geometric Ergodicity of Gibbs and Block Gibbs Samplers for a Hierarchical Random Effects Model," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 414-430, November.
    • Handle: RePEc:eee:jmvana:v:67:y:1998:i:2:p:414-430
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    References listed on IDEAS

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    1. G. O. Roberts & S. K. Sahu, 1997. "Updating Schemes, Correlation Structure, Blocking and Parameterization for the Gibbs Sampler," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(2), pages 291-317.
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    1. Wilkinson, Darren J & KH Yeung, Stephen, 2004. "A sparse matrix approach to Bayesian computation in large linear models," Computational Statistics & Data Analysis, Elsevier, vol. 44(3), pages 493-516, January.
    2. Mogliani, Matteo & Simoni, Anna, 2021. "Bayesian MIDAS penalized regressions: Estimation, selection, and prediction," Journal of Econometrics, Elsevier, vol. 222(1), pages 833-860.
    3. 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.
    4. Korobilis, Dimitris, 2013. "Hierarchical shrinkage priors for dynamic regressions with many predictors," International Journal of Forecasting, Elsevier, vol. 29(1), pages 43-59.
    5. De la Cruz, Rolando & Meza, Cristian & Arribas-Gil, Ana & Carroll, Raymond J., 2016. "Bayesian regression analysis of data with random effects covariates from nonlinear longitudinal measurements," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 94-106.

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