IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-4-431-54574-3_4.html
   My bibliography  Save this book chapter

Markov Bases and Designed Experiments

In: Gröbner Bases

Author

Listed:
  • Satoshi Aoki

    (Kagoshima University, Department of Mathematics and Computer Science)

  • Akimichi Takemura

    (University of Tokyo, Department of Mathematical Informatics, Graduate School of Information Science and Technology)

Abstract

Markov bases first appeared in a 1998 work by Diaconis and Sturmfels (Ann Stat 26:363–397, 1998). In this paper, they considered the problem of estimating the p values for conditional tests for data summarized in contingency tables by Markov chain Monte Carlo methods; this is one of the fundamental problems in applied statistics. In this setting, it is necessary to have an appropriate connected Markov chain over the given finite sample space. Diaconis and Sturmfels formulated this problem with the idea of a Markov basis, and they showed that it corresponds to the set of generators of a well-specified toric ideal. Their work is very attractive because the theory of a Gröbner basis, a concept of pure mathematics, can be used in actual problems in applied statistics. In fact, their work became one of the origins of the relatively new field, computational algebraic statistics. In this chapter, we first introduce their work along with the necessary background in statistics. After that, we use the theory of Gröbner bases to solve actual applied statistical problems in experimental design.

Suggested Citation

  • Satoshi Aoki & Akimichi Takemura, 2013. "Markov Bases and Designed Experiments," Springer Books, in: Takayuki Hibi (ed.), Gröbner Bases, edition 127, chapter 0, pages 165-221, Springer.
    • Handle: RePEc:spr:sprchp:978-4-431-54574-3_4
    DOI: 10.1007/978-4-431-54574-3_4
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:sprchp:978-4-431-54574-3_4. 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.