Exchangeable random variables

Summary

A finite or infinite sequence of random variables is exchangeable when its joint distribution does not change if finitely many of the variables are permuted. Every sequence of independent and identically distributed random variables is exchangeable, but exchangeable variables need not be independent. Exchangeability is the basic symmetry assumption of Bayesian statistics. By de Finetti's theorem, an infinite exchangeable sequence is a mixture of i.i.d. sequences.