Abstract
Abstract In probability theory, the random variables Y 1 , …, Y N are said to be exchangeable (or permutable or symmetric ) if their joint distribution F ( y 1 , …, y N ) is symmetric; that is, if F is invariant under permutation of its arguments, so that whenever z 1 , …, z N is a permutation of y 1 , …, y N . There is a related epidemiologic usage, which is described in the article on confounding. In many ways, sequences of exchangeable random variables play a role in subjective Bayesian theory analogous to that played by independent identically distributed (iid) sequences in classical frequentist theory. In particular, the assumption that a sequence of random variables is exchangeable allows the development of inductive statistical procedures for inference from observed to unobserved members of the sequence [1, 2, 3, 5, 6, 9].
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