We describe new families of discrete distributions that are used to model sums of exchangeable Bernoulli random variables. These discrete distributions can be parameterized in terms of their range, ...

ABSTRACT: We study the connection between the central limit theorem and law of large numbers for exchangeable sequences, and provide a counterexample to the Gnedenko-Raikov theorem for such sequences.

Department of Mathematical Sciences, Lakehead University, Thunder Bay, Canada. Department of Mathematical Sciences, University of New Brunswick, Saint John, Canada. The celebrated Gnedenko-Raikov ...

Exchangeability refers to the property of a sequence or collection of random variables whereby its joint probability distribution remains unchanged under any finite permutation of indices. This ...

This lecture studies learning via Bayes' Law. We touch foundations of Bayesian statistical inference invented by Bruno DeFinetti {cite}definetti. The relevance of DeFinetti's work for economists is ...

Abstract: We review information-theoretic approaches to obtaining simple probabilistic representations for sequences of exchangeable random variables. Specifically, we examine information-theoretic ...

Abstract: Wyner defined the notion of common information of two discrete random variables as the minimum of I(W; X,Y) where W induces conditional independence between X and Y. Its generalization to ...

A finite set of random variables $\lbrace X_1,\ldots,X_n \rbrace$ defined on a common probablility space $(\Omega, \mathcal{F}, P)$ is said to be \emph{exchangeable ...