IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v66y2014i1p63-74.html
   My bibliography  Save this article

Local consistency of Markov chain Monte Carlo methods

Author

Listed:
  • Kengo Kamatani

Abstract

In this paper, we introduce the notion of efficiency (consistency) and examine some asymptotic properties of Markov chain Monte Carlo methods. We apply these results to the data augmentation (DA) procedure for independent and identically distributed observations. More precisely, we show that if both the sample size and the running time of the DA procedure tend to infinity, the empirical distribution of the DA procedure tends to the posterior distribution. This is a local property of the DA procedure, which may be, in some cases, more helpful than the global properties to describe its behavior. The advantages of using the local properties are the simplicity and the generality of the results. The local properties provide useful insight into the problem of how to construct efficient algorithms. Copyright The Institute of Statistical Mathematics, Tokyo 2014

Suggested Citation

  • Kengo Kamatani, 2014. "Local consistency of Markov chain Monte Carlo methods," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(1), pages 63-74, February.
    • Handle: RePEc:spr:aistmt:v:66:y:2014:i:1:p:63-74
    DOI: 10.1007/s10463-013-0403-3
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10463-013-0403-3
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10463-013-0403-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

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

    Citations

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


    Cited by:

    1. Kamatani, Kengo, 2020. "Random walk Metropolis algorithm in high dimension with non-Gaussian target distributions," Stochastic Processes and their Applications, Elsevier, vol. 130(1), pages 297-327.

    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:spr:aistmt:v:66:y:2014:i:1:p:63-74. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.