IDEAS home Printed from
   My bibliography  Save this article

Optimizing random scan Gibbs samplers


  • Levine, Richard A.
  • Casella, George


The Gibbs sampler is a popular Markov chain Monte Carlo routine for generating random variates from distributions otherwise difficult to sample. A number of implementations are available for running a Gibbs sampler varying in the order through which the full conditional distributions used by the Gibbs sampler are cycled or visited. A common, and in fact the original, implementation is the random scan strategy, whereby the full conditional distributions are updated in a randomly selected order each iteration. In this paper, we introduce a random scan Gibbs sampler which adaptively updates the selection probabilities or "learns" from all previous random variates generated during the Gibbs sampling. In the process, we outline a number of variations on the random scan Gibbs sampler which allows the practitioner many choices for setting the selection probabilities and prove convergence of the induced (Markov) chain to the stationary distribution of interest. Though we emphasize flexibility in user choice and specification of these random scan algorithms, we present a minimax random scan which determines the selection probabilities through decision theoretic considerations on the precision of estimators of interest. We illustrate and apply the results presented by using the adaptive random scan Gibbs sampler developed to sample from multivariate Gaussian target distributions, to automate samplers for posterior simulation under Dirichlet process mixture models, and to fit mixtures of distributions.

Suggested Citation

  • Levine, Richard A. & Casella, George, 2006. "Optimizing random scan Gibbs samplers," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2071-2100, November.
  • Handle: RePEc:eee:jmvana:v:97:y:2006:i:10:p:2071-2100

    Download full text from publisher

    File URL:
    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

    1. Amit, Y. & Grenander, U., 1991. "Comparing sweep strategies for stochastic relaxation," Journal of Multivariate Analysis, Elsevier, vol. 37(2), pages 197-222, May.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:

    1. 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.
    2. Chen, Shyh-Huei & Ip, Edward H. & Wang, Yuchung J., 2011. "Gibbs ensembles for nearly compatible and incompatible conditional models," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1760-1769, April.


    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:97:y:2006:i:10:p:2071-2100. 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: .

    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.