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.
Facts
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 Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
In Branch
Source De Finetti's theorem, Wikipedia
Principal Result Of
Source Bruno de Finetti (Wikipedia)
Proved By
Source De Finetti's theorem, Wikipedia
Sources
1. De Finetti's theorem, Wikipedia
Statement of the theorem
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.
Proved By: Bruno de Finetti, Lead sentence
It is named in honor of Bruno de Finetti, and one of its uses is in providing a pragmatic approach to de Finetti's well-known dictum "Probability does not exist".
In Branch: Probability and Statistics, Lead sentence
In probability theory, de Finetti's theorem states that exchangeable observations are conditionally independent relative to some l
In Group: Probability Theory, Lead section
In probability theory, de Finetti's theorem states that exchangeable
View the SourceBruno de Finetti (Wikipedia)
Principal Result Of: Bruno de Finetti, Work and impact, exchangeable sequencesQuote, Principal Result Of: Bruno de Finetti, Work and impact, exchangeable sequences
De Finetti is also noted for de Finetti's theorem on exchangeable sequences of random variables.
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