IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this paper

Improving the Convergence Properties of the Data Augmentation Algorithm with an Application to Bayesian Mixture Modelling

Listed author(s):
  • James P. Hobert


  • Christian P. Robert


  • Vivekanada Roy


Registered author(s):

    Every reversible Markov chain defines an operator whose spectrum encodes the convergenceproperties of the chain. When the state space is finite, the spectrum is just the set ofeigenvalues of the corresponding Markov transition matrix. However, when the state space isinfinite, the spectrum may be uncountable, and is nearly always impossible to calculate. In mostapplications of the data augmentation (DA) algorithm, the state space of the DA Markov chainis infinite. However, we show that, under regularity conditions that include the finiteness of theaugmented space, the operators defined by the DA chain and Hobert and Marchev’s (2008) alternativechain are both compact, and the corresponding spectra are both finite subsets of [0; 1).Moreover, we prove that the spectrum of Hobert and Marchev’s (2008) chain dominates thespectrum of the DA chain in the sense that the ordered elements of the former are all less thanor equal to the corresponding elements of the latter. As a concrete example, we study a widelyused DA algorithm for the exploration of posterior densities associated with Bayesian mixturemodels (Diebolt and Robert, 1994). In particular, we compare this mixture DA algorithm withan alternative algorithm proposed by Fr¨uhwirth-Schnatter (2001) that is based on random labelswitching.

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

    File URL:
    File Function: Crest working paper version
    Download Restriction: no

    Paper provided by Center for Research in Economics and Statistics in its series Working Papers with number 2010-29.

    in new window

    Length: 38
    Date of creation: 2010
    Handle: RePEc:crs:wpaper:2010-29
    Contact details of provider: Postal:
    Bâtiment ENSAE, 5 rue Henry LE Chatelier, 91120 Palaiseau

    Phone: 01 41 17 60 81
    Web page:

    More information through EDIRC

    No references listed on IDEAS
    You can help add them by filling out this form.

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:crs:wpaper:2010-29. 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: (Sri Srikandan)

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 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.

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.