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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
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    References listed on IDEAS

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    1. von Plato, Jan, 1991. "Finite partial exchangeability," Statistics & Probability Letters, Elsevier, vol. 11(2), pages 99-102, February.
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    Cited by:

    1. Fabio Vanni & David Lambert, 2024. "Aging Renewal Point Processes and Exchangeability of Event Times," Mathematics, MDPI, vol. 12(10), pages 1-26, May.

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