Electronic Journal of Statistics
- Electron. J. Statist.
- Volume 7 (2013), 2193-2208.
Exchangeable Bernoulli random variables and Bayes’ postulate
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.
Electron. J. Statist., Volume 7 (2013), 2193-2208.
First available in Project Euclid: 16 September 2013
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62A01: Foundations and philosophical topics
Secondary: 62C10: Bayesian problems; characterization of Bayes procedures
Banerjee, Moulinath; Richardson, Thomas. Exchangeable Bernoulli random variables and Bayes’ postulate. Electron. J. Statist. 7 (2013), 2193--2208. doi:10.1214/13-EJS835. https://projecteuclid.org/euclid.ejs/1379336968