Probability Theory pp 231-243 | Cite as

# Backwards Martingales and Exchangeability

Chapter

With many data acquisitions, such as telephone surveys, the order in which the data come does not matter. Mathematically, we say that a family of random variables is *exchangeable* if the joint distribution does not change under finite permutations. De Finetti’s structural theorem says that an infinite family of *E*-valued exchangeable random variables can be described by a two-stage experiment. At the first stage, a probability distribution Ξ on *E* is drawn at random. At the second stage, i.i.d. random variables with distribution Ξ are implemented.

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