IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v19y2006i3d10.1007_s10959-006-0028-z.html
   My bibliography  Save this article

Definetti’s Theorem for Abstract Finite Exchangeable Sequences

Author

Listed:
  • G. Jay. Kerns

    (Youngstown State University)

  • Gábor J. Székely

    (Bowling Green State University
    Hungarian Academy of Sciences)

Abstract

We show that a finite collection of exchangeable random variables on an arbitrary measurable space is a signed mixture of i.i.d. random variables. Two applications of this idea are examined, one concerning Bayesian consistency, in which it is established that a sequence of posterior distributions continues to converge to the true value of a parameter θ under much wider assumptions than are ordinarily supposed, the next pertaining to Statistical Physics where it is demonstrated that the quantum statistics of Fermi-Dirac may be derived from the statistics of classical (i.e. independent) particles by means of a signed mixture of multinomial distributions.

Suggested Citation

  • G. Jay. Kerns & Gábor J. Székely, 2006. "Definetti’s Theorem for Abstract Finite Exchangeable Sequences," Journal of Theoretical Probability, Springer, vol. 19(3), pages 589-608, December.
    • Handle: RePEc:spr:jotpro:v:19:y:2006:i:3:d:10.1007_s10959-006-0028-z
    DOI: 10.1007/s10959-006-0028-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-006-0028-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10959-006-0028-z?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.

    References listed on IDEAS

    as
    1. von Plato, Jan, 1991. "Finite partial exchangeability," Statistics & Probability Letters, Elsevier, vol. 11(2), pages 99-102, February.
    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. Fabio Vanni & David Lambert, 2024. "Aging Renewal Point Processes and Exchangeability of Event Times," Mathematics, MDPI, vol. 12(10), pages 1-27, May.

    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. Gnedin, Alexander V., 1995. "On a class of exchangeable sequences," Statistics & Probability Letters, Elsevier, vol. 25(4), pages 351-355, December.
    2. Paolo Leonetti, 2018. "Finite Partially Exchangeable Laws Are Signed Mixtures of Product Laws," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(2), pages 195-214, August.
    3. Gnedin, Alexander V., 1996. "A class of exchangeable sequences," Statistics & Probability Letters, Elsevier, vol. 28(2), pages 159-164, June.

    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:jotpro:v:19:y:2006:i:3:d:10.1007_s10959-006-0028-z. 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: 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.