Bayesian Statisticians, decision theorists, and game theorists often use Bayesian representations to describe the probability distribution governing the evolution of a stochastic process. Generally, however, one given distribution has infinitely many different Bayesian representations. This paper identifies natural, endogenous representations whose component distributions are learnable and follow patterns. Any given distribution that satisfies an asymptotic mixing condition has a unique, up to an equivalence class, natural Bayesian representation which can be obtained by conditioning on the tail-field of the process. This result follows a parallel to de Finetti's theorem, but with exchangeability weakened to asymptotic mixing which admits many more applications.
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Length: 27 pages Date of creation: 25 Nov 1997 Date of revision: Handle: RePEc:wpa:wuwpga:9711002
Note: Type of Document - postscript; prepared on gateway e 3100; to print on postscript; pages: 27 ; figures: none. comments welcome Contact details of provider: Web page: http://129.3.20.41
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Matthew O. Jackson & Ehud Kalai & Rann Smorodinsky, 1997.
"Patterns, Types, and Bayesian Learning,"
Discussion Papers
1177, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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Find related papers by JEL classification: C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Bayesian Analysis D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information
References listed on IDEAS Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
Matthew Jackson & Ehud Kalai, 1995.
"Social Learning in Recurring Games,"
Discussion Papers
1138, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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