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November, 1974 Bayesian Reconstructions of $m, n$-Patterns
Marc Moore
Ann. Statist. 2(6): 1226-1237 (November, 1974). DOI: 10.1214/aos/1176342875


The notion of $m, n$-pattern is introduced--namely, a division of the unit interval into at most $n$ cells (intervals or points), each having one of $m$ colors. Given an unknown $m, n$ pattern, it is desired to produce a reconstruction of the pattern using $r \geqq 1$ sample points (fixed or chosen at random) where the color is determined. The problem is studied from a decision-theoretic point of view. A way to obtain all the probability measures on the set of $m, n$-patterns is given. The notion of a Bayesian reconstruction rule (B.R.R.) is introduced. It is proved that when B.R.R.'s are considered, it is sufficient to use certain fixed sample points. A complete class of reconstruction rules is obtained. Finally an example of a B.R.R. is given for 2,2-patterns.


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Marc Moore. "Bayesian Reconstructions of $m, n$-Patterns." Ann. Statist. 2 (6) 1226 - 1237, November, 1974.


Published: November, 1974
First available in Project Euclid: 12 April 2007

zbMATH: 0297.62005
MathSciNet: MR362589
Digital Object Identifier: 10.1214/aos/1176342875

Primary: 62C10
Secondary: 62C07 , 62C99 , 62F99

Keywords: Bayes , cell , color , measure , Pattern , reconstruction rule , sample points , Wald's decision theory

Rights: Copyright © 1974 Institute of Mathematical Statistics


Vol.2 • No. 6 • November, 1974
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