De Finetti's Theorem states that an infinite sequence of exchangeable random variables, meaning its joint distribution is unchanged by any reordering of finitely many terms, can always be represented as a mixture of sequences of independent and identically distributed random variables, conditioned on an underlying random parameter. Named for Bruno de Finetti, it is a foundational result of probability theory providing a rigorous basis for the Bayesian interpretation of exchangeable data as arising from an unknown but fixed underlying probability.
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StatementDe Finetti's theorem states that the probability distribution of any infinite exchangeable sequence of Bernoulli random variables is a mixture of the probability distributions of independent and identically distributed sequences of Bernoulli random variables. 1 Sources
1. De Finetti's theorem, Wikipedia
Lead sectionQuote, Lead section
De Finetti's theorem states that the probability distribution of any infinite exchangeable sequence of Bernoulli random variables is a mixture of the probability distributions of independent and identically distributed sequences of Bernoulli random variables.
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