Abstract
A prior distribution ∧ on a set of parameters I is said to be ergodically decomposable if ∧ - a. all probability measures (πi)i∈I are mutually singular in some strong sense. Criteria are established for ∧ 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 πi the Poisson process with intensity i, is just the Papangelou kernel of the Cox process directed by ∧.
Citation
E. Glotzl. A. Wakolbinger. "Bayes Estimators and Ergodic Decomposability with an Application to Cox Processes." Ann. Probab. 10 (3) 872 - 876, August, 1982. https://doi.org/10.1214/aop/1176993801
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