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2013 Exchangeable Bernoulli random variables and Bayes’ postulate
Moulinath Banerjee, Thomas Richardson
Electron. J. Statist. 7: 2193-2208 (2013). DOI: 10.1214/13-EJS835


We discuss the implications of Bayes’ postulate in the setting of exchangeable Bernoulli random variables. Bayes’ postulate, here, stipulates a uniform distribution on the total number of successes in any number of trials. For an infinite sequence of exchangeable Bernoulli variables the conditions of Bayes’ postulate are equivalent to a uniform (prior) distribution on the underlying mixing variable which necessarily exists by De Finetti’s representation theorem. We show that in the presence of exchangeability, the conditions of Bayes’ postulate are implied by a considerably weaker assumption which only specifies the probability of $n$ successes in $n$ trials, for every $n$. The equivalence of the Bayes’ postulate and the weak assumption holds for both finite and infinite sequences. We also explore characterizations of the joint distribution of finitely many exchangeable Bernoulli variables in terms of probability statements similar to the weak assumption. Finally, we consider extensions of Bayes’ postulate in the framework of exchangeable multinomial trials.


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Moulinath Banerjee. Thomas Richardson. "Exchangeable Bernoulli random variables and Bayes’ postulate." Electron. J. Statist. 7 2193 - 2208, 2013.


Published: 2013
First available in Project Euclid: 16 September 2013

zbMATH: 1293.62007
MathSciNet: MR3104917
Digital Object Identifier: 10.1214/13-EJS835

Primary: 62A01
Secondary: 62C10

Keywords: Bayes’ postulate , Bernoulli random variables , exchangeability , multinomial trials , weak assumption

Rights: Copyright © 2013 The Institute of Mathematical Statistics and the Bernoulli Society


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