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In statistics, an exchangeable sequence of random variables (also sometimes interchangeable)〔 is a sequence such that future samples behave like earlier samples, meaning formally that any order (of a finite number of samples) is equally likely. This formalizes the notion of "the future being predictable on the basis of past experience." It is closely related to the use of independent and identically-distributed random variables in statistical models. Exchangeable sequences of random variables arise in cases of simple random sampling. == Definition == Formally, an exchangeable sequence of random variables is a finite or infinite sequence ''X''1, ''X''2, ''X''3, ... of random variables such that for any finite permutation σ of the indices 1, 2, 3, ..., (the permutation acts on only finitely many indices, with the rest fixed), the joint probability distribution of the permuted sequence : is the same as the joint probability distribution of the original sequence.〔In short, the order of the sequence of random variables does not affect its joint probability distribution. * Chow, Yuan Shih and Teicher, Henry, ''Probability theory. Independence, interchangeability, martingales,'' Springer Texts in Statistics, 3rd ed., Springer, New York, 1997. xxii+488 pp. ISBN 0-387-98228-0〕〔Aldous, David J., ''Exchangeability and related topics'', in: École d'Été de Probabilités de Saint-Flour XIII — 1983, Lecture Notes in Math. 1117, pp. 1–198, Springer, Berlin, 1985. ISBN 978-3-540-15203-3 〕 (A sequence ''E''1, ''E''2, ''E''3, ... of events is said to be exchangeable precisely if the sequence of its indicator functions is exchangeable.) The distribution function ''F''''X''''1'',...,''X''''n''(''x''1, ..., ''x''''n'') of a finite sequence of exchangeable random variables is symmetric in its arguments Olav Kallenberg provided an appropriate definition of exchangeability for continuous-time stochastic processes.〔Kallenberg, O., ''Probabilistic symmetries and invariance principles''. Springer-Verlag, New York (2005). 510 pp. ISBN 0-387-25115-4.〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Exchangeable random variables」の詳細全文を読む スポンサード リンク
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