IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v67y1998i2p414-430.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(98)91778-X
    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. 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.
    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. Korobilis, Dimitris, 2013. "Hierarchical shrinkage priors for dynamic regressions with many predictors," International Journal of Forecasting, Elsevier, vol. 29(1), pages 43-59.
    2. 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.
    3. Mogliani, Matteo & Simoni, Anna, 2021. "Bayesian MIDAS penalized regressions: Estimation, selection, and prediction," Journal of Econometrics, Elsevier, vol. 222(1), pages 833-860.
    4. 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.
    5. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Billio, Monica & Casarin, Roberto & Osuntuyi, Anthony, 2016. "Efficient Gibbs sampling for Markov switching GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 37-57.
    2. Strickland, Chris M. & Martin, Gael M. & Forbes, Catherine S., 2008. "Parameterisation and efficient MCMC estimation of non-Gaussian state space models," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 2911-2930, February.
    3. Ahelegbey, Daniel Felix & Giudici, Paolo & Hashem, Shatha Qamhieh, 2021. "Network VAR models to measure financial contagion," The North American Journal of Economics and Finance, Elsevier, vol. 55(C).
    4. Pasanisi, Alberto & Fu, Shuai & Bousquet, Nicolas, 2012. "Estimating discrete Markov models from various incomplete data schemes," Computational Statistics & Data Analysis, Elsevier, vol. 56(9), pages 2609-2625.
    5. Gael M. Martin & David T. Frazier & Christian P. Robert, 2020. "Computing Bayes: Bayesian Computation from 1763 to the 21st Century," Monash Econometrics and Business Statistics Working Papers 14/20, Monash University, Department of Econometrics and Business Statistics.
    6. Gael M. Martin & David T. Frazier & Ruben Loaiza-Maya & Florian Huber & Gary Koop & John Maheu & Didier Nibbering & Anastasios Panagiotelis, 2023. "Bayesian Forecasting in the 21st Century: A Modern Review," Monash Econometrics and Business Statistics Working Papers 1/23, Monash University, Department of Econometrics and Business Statistics.
    7. Jeffrey Rouder & Jordan Province & Richard Morey & Pablo Gomez & Andrew Heathcote, 2015. "The Lognormal Race: A Cognitive-Process Model of Choice and Latency with Desirable Psychometric Properties," Psychometrika, Springer;The Psychometric Society, vol. 80(2), pages 491-513, June.
    8. Zhang, Xiao & Boscardin, W. John & Belin, Thomas R. & Wan, Xiaohai & He, Yulei & Zhang, Kui, 2015. "A Bayesian method for analyzing combinations of continuous, ordinal, and nominal categorical data with missing values," Journal of Multivariate Analysis, Elsevier, vol. 135(C), pages 43-58.
    9. Yin, Libo & Ma, Xiyuan, 2018. "Causality between oil shocks and exchange rate: A Bayesian, graph-based VAR approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 434-453.
    10. MacEachern, Steven N. & Peruggia, Mario, 2000. "Subsampling the Gibbs sampler: variance reduction," Statistics & Probability Letters, Elsevier, vol. 47(1), pages 91-98, March.
    11. Håvard Rue & Ingelin Steinsland & Sveinung Erland, 2004. "Approximating hidden Gaussian Markov random fields," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(4), pages 877-892, November.
    12. Hongju Liu & Qiang Liu & Pradeep K. Chintagunta, 2017. "Promotion Spillovers: Drug Detailing in Combination Therapy," Marketing Science, INFORMS, vol. 36(3), pages 382-401, May.
    13. Marcin Mider & Paul A. Jenkins & Murray Pollock & Gareth O. Roberts, 2022. "The Computational Cost of Blocking for Sampling Discretely Observed Diffusions," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 3007-3027, December.
    14. Levine, Richard A. & Yu, Zhaoxia & Hanley, William G. & Nitao, John J., 2005. "Implementing componentwise Hastings algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 48(2), pages 363-389, February.
    15. Sanjay Chaudhuri, 2014. "Qualitative inequalities for squared partial correlations of a Gaussian random vector," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(2), pages 345-367, April.
    16. Barone, Piero & Sebastiani, Giovanni & Stander, Julian, 2001. "General over-relaxation Markov chain Monte Carlo algorithms for Gaussian densities," Statistics & Probability Letters, Elsevier, vol. 52(2), pages 115-124, April.
    17. Wong, Jackie S.T. & Forster, Jonathan J. & Smith, Peter W.F., 2018. "Bayesian mortality forecasting with overdispersion," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 206-221.
    18. Ahelegbey, Daniel Felix & Giudici, Paolo, 2022. "NetVIX — A network volatility index of financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 594(C).
    19. Bianchi, Daniele & Billio, Monica & Casarin, Roberto & Guidolin, Massimo, 2019. "Modeling systemic risk with Markov Switching Graphical SUR models," Journal of Econometrics, Elsevier, vol. 210(1), pages 58-74.
    20. Gschlößl, Susanne & Czado, Claudia, 2008. "Does a Gibbs sampler approach to spatial Poisson regression models outperform a single site MH sampler?," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4184-4202, May.

    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:67:y:1998:i:2:p:414-430. See general information about how to correct material in RePEc.

    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 bibliographic 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.

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

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.