Exchangeable random variables: Difference between revisions

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== History ==
The concept was introduced by [[William Ernest Johnson]] in his 1924 book ''Logic, Part III: The Logical Foundations of Science''.<ref>Zabell{{ (cite journal | title=Predicting the unpredictable | year=1992) | journal=Synthese | volume=90 | issue=2 | page=205 | doi=10.1007/bf00485351 | last1=Zabell | first1=S. L. | s2cid=9416747 }}</ref> Exchangeability is equivalent to the concept of [[statistical control]] introduced by [[Walter Shewhart]] also in 1924.<ref>Barlow, R. E. & Irony, T. Z. (1992) "Foundations of statistical quality control" in Ghosh, M. & Pathak, P.K. (eds.) ''Current Issues in Statistical Inference: Essays in Honor of D. Basu'', Hayward, CA: Institute of Mathematical Statistics, 99-112.</ref><ref>Bergman, B. (2009) "Conceptualistic Pragmatism: A framework for Bayesian analysis?", ''IIE Transactions'', '''41''', 86–93</ref>
 
== Exchangeability and the i.i.d. statistical model ==
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* {{sectionlink|Resampling (statistics)|Permutation tests}}, statistical tests based on exchanging between groups
 
==Notes Refererences ==
{{Reflist}}
<references/>
 
== BibliographyFurther reading ==
* Aldous, David J., ''Exchangeability and related topics'', in: École d'Été de Probabilités de Saint-Flour XIII — 1983, Lecture Notes in Math. 1117, pp.&nbsp;1–198, Springer, Berlin, 1985. {{ISBN|978-3-540-15203-3}} {{doi|10.1007/BFb0099421}}
* Barlow, R. E. & Irony, T. Z. (1992) "Foundations of statistical quality control" in Ghosh, M. & Pathak, P.K. (eds.) ''Current Issues in Statistical Inference: Essays in Honor of D. Basu'', Hayward, CA: Institute of Mathematical Statistics, 99-112.
* Bergman, B. (2009) "Conceptualistic Pragmatism: A framework for Bayesian analysis?", ''IIE Transactions'', '''41''', 86–93
* {{cite book |last=Borovskikh | first=Yu. V. | title=''U''-statistics in Banach spaces | publisher=VSP | ___location=Utrecht | year=1996 | pages=xii+420 | isbn=90-6764-200-2 | mr=1419498 }}
* Chow, Yuan Shih and Teicher, Henry, ''Probability theory. Independence, interchangeability, martingales,'' Springer Texts in Statistics, 3rd ed., Springer, New York, 1997. xxii+488 pp.&nbsp;{{ISBN|0-387-98228-0}}
* {{cite book |last=Dawid |first=A. Philip |chapter=Exchangeability and its ramifications |pages=19–30 |title=Bayesian Theory and Applications |editor-first=Paul |editor-last=Damien |editor2-first=Petros |editor2-last=Dellaportas |editor3-first=Nicholas G. |editor3-last=Polson |editor4-first=David A. |editor4-last=Stephens |display-editors=1 |publisher=Oxford University Press |year=2013 |isbn=978-0-19-969560-7 }}
* {{cite journal | last=Diaconis| first=Persi | author-link=Persi Diaconis | title=Book review: ''Probabilistic symmetries and invariance principles'' (Olav Kallenberg, Springer, New York, 2005) | journal=Bulletin of the American Mathematical Society |series=New Series | volume=46 | year=2009 | issue=4 | doi=10.1090/S0273-0979-09-01262-2 | pages=691–696 | mr=2525743| doi-access=free }}
* [[Olav Kallenberg|Kallenberg, O.]], ''Probabilistic symmetries and invariance principles''. Springer-Verlag, New York (2005). 510 pp.&nbsp;{{ISBN|0-387-25115-4}}.
* Kingman, J. F. C., ''Uses of exchangeability'', Ann. Probability 6 (1978) 83&ndash;197 {{MR|494344}} {{JSTOR|2243211}}
* O'Neill, B. (2009) Exchangeability, Correlation and Bayes' Effect. ''International Statistical Review'' '''77(2)''', pp.&nbsp;241–250. {{ISBN|978-3-540-15203-3}} {{doi|10.1111/j.1751-5823.2008.00059.x}}
* {{cite book|title=Limit theorems for sums of exchangeable random&nbsp;variables|first1=Robert Lee|last1=Taylor|first2=Peter Z.|last2=Daffer|first3=Ronald F.|last3=Patterson|publisher=Rowman and Allanheld|url=https://books.google.com/books?id=6RaoAAAAIAAJ|year=1985|pages=1–152|isbn=9780847674350}}
* Zabell, S. L. (1988) "Symmetry and its discontents", in Skyrms, B. & Harper, W. L. ''Causation, Chance and Credence, ''pp''155-190, Kluwer
* {{ cite journal | title=Predicting the unpredictable | year=1992 | journal=Synthese | volume=90 | issue=2 | page=205 | doi=10.1007/bf00485351 | last1=Zabell | first1=S. L. | s2cid=9416747 }}
 
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