Definetti’s Theorem for Abstract Finite Exchangeable Sequences

G. Jay. Kerns () and Gábor J. Székely ()
Additional contact information
G. Jay. Kerns: Youngstown State University
Gábor J. Székely: Bowling Green State University

Journal of Theoretical Probability, 2006, vol. 19, issue 3, 589-608

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.

Keywords: Exchangeable variables; de Finetti’s theorem; finite exchangeable sequence; signed measure; extreme points; Primary: 60B05; Secondary: 60E99; Secondary: 62E99 (search for similar items in EconPapers)
Date: 2006
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10959-006-0028-z Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:19:y:2006:i:3:d:10.1007_s10959-006-0028-z

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-006-0028-z

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().