IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v140y2015icp325-342.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X15001451
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Vivekananda Roy & James P. Hobert, 2007. "Convergence rates and asymptotic standard errors for Markov chain Monte Carlo algorithms for Bayesian probit regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 607-623, September.
    2. Jones, Galin L. & Haran, Murali & Caffo, Brian S. & Neath, Ronald, 2006. "Fixed-Width Output Analysis for Markov Chain Monte Carlo," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1537-1547, December.
    3. James P. Hobert, 2002. "On the applicability of regenerative simulation in Markov chain Monte Carlo," Biometrika, Biometrika Trust, vol. 89(4), pages 731-743, December.
    4. Levine, Richard A. & Casella, George, 2006. "Optimizing random scan Gibbs samplers," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2071-2100, November.
    5. Gareth O. Roberts & Jeffrey S. Rosenthal, 1999. "Convergence of Slice Sampler Markov Chains," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 643-660.
    6. 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.
    7. Marchev, Dobrin & Hobert, James P., 2004. "Geometric Ergodicity of van Dyk and Meng's Algorithm for the Multivariate Student's t Model," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 228-238, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:140:y:2015:i:c:p:325-342. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.