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A sequence of [[independent and identically-distributed random variables]] (i.i.d.) is exchangeable, but so is [[simple random sample without replacement|sampling without replacement]], which is not independent.
The notion is central to [[Bruno de Finetti|Bruno de Finetti's]] development of [[predictive inference]] and to [[Bayesian statistics]] – where [[frequentist statistics]] uses i.i.d. variables (samples from a population), Bayesian statistics more frequently uses exchangeable sequences. They are a key way in which Bayesian inference is "data-centric" (based on past and future observations), rather than "model-centric", as exchangeable sequences that are not i.i.d. cannot be modeled as "sampling from a fixed population".
== Definition ==
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