Original sentence: A related notion to exchangeability, also championed by de Finetti, is of predictive inference – an interpretation of probability that emphasizes the role of prediction, predicting future observations on the basis of past observations, not on unobservable parameters.As future values of exchangeable sequences behave like past ones, they are precisely the sequences on which (stationary) statistics works.Exchangeability means that while variables may not be independent, future ones behave like past ones – formally, any value of a finite sequence is as likely as any permutation of those values – the joint probability distribution is invariant under the symmetric group.In Bayesian statistics, the notion of independent and identically-distributed random variables is often replaced by the generalization to exchangeable random variables, introduced by Bruno de Finetti.In its modern form, it is mainly in the Bayesian vein.This provides a useful generalization – for example, sampling without replacement is not independent, but is exchangeable – and is 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.cannot be modeled as "sampling from a fixed population"