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August, 1982 Bayes Estimators and Ergodic Decomposability with an Application to Cox Processes
E. Glotzl, A. Wakolbinger
Ann. Probab. 10(3): 872-876 (August, 1982). DOI: 10.1214/aop/1176993801


A prior distribution $\wedge$ on a set of parameters $I$ is said to be ergodically decomposable if $\wedge$ - a. all probability measures $(\pi_i)_{i\in I}$ are mutually singular in some strong sense. Criteria are established for $\wedge$ to be ergodically decomposable in terms of the posterior distribution and the Bayes estimator, which, for $I$ the locally finite measures on a Polish space and $\pi_i$ the Poisson process with intensity $i$, is just the Papangelou kernel of the Cox process directed by $\wedge$.


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E. Glotzl. A. Wakolbinger. "Bayes Estimators and Ergodic Decomposability with an Application to Cox Processes." Ann. Probab. 10 (3) 872 - 876, August, 1982.


Published: August, 1982
First available in Project Euclid: 19 April 2007

MathSciNet: MR659560
Digital Object Identifier: 10.1214/aop/1176993801

Primary: 60K99
Secondary: 62A15 , 62B20

Keywords: Bayes estimator , Cox processes , ergodic decomposability , extreme points , Papangelou kernel , sufficient statistics

Rights: Copyright © 1982 Institute of Mathematical Statistics


Vol.10 • No. 3 • August, 1982
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