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Journal of Theoretical Probability

, Volume 19, Issue 3, pp 589–608 | Cite as

Definetti’s Theorem for Abstract Finite Exchangeable Sequences

  • G. Jay. Kerns
  • Gábor J. SzékelyEmail author
Article

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 

2000 Mathematical Subject Classification

Primary: 60B05 Secondary: 60E99 Secondary: 62E99 

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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsYoungstown State UniversityYoungstownUSA
  2. 2.Department of Mathematics and StatisticsBowling Green State UniversityBowling GreenUSA
  3. 3.Renyi Institute of MathematicsHungarian Academy of SciencesBudapestHungary

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