Open Access
June 1996 On the existence of inferences which are consistent with a given model
Patrizia Berti, Pietro Rigo
Ann. Statist. 24(3): 1235-1249 (June 1996). DOI: 10.1214/aos/1032526966


4 If ${p_{\theta}$ is a $\sigma$-additive statistical model and $\pi$ a finitely additive prior, then any statistic T is sufficient, with respect to a suitable inference consistent with ${p_{\theta}$ and $\pi$, provided only that $p_{\theta}(T = t) = 0$ for all $\theta$ and t. Here, sufficiency is to be intended in the Bayesian sense, and consistency in the sense of Lane and Sudderth. As a corollary, if ${p_{\theta}$ is $\sigma$-additive and diffuse, then, whatever the prior $\pi$, there is an inference which is consistent with ${p_{\theta}$ and $\pi$. Two versions of the main result are also obtained for predictive problems.


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Patrizia Berti. Pietro Rigo. "On the existence of inferences which are consistent with a given model." Ann. Statist. 24 (3) 1235 - 1249, June 1996.


Published: June 1996
First available in Project Euclid: 20 September 2002

zbMATH: 0866.62001
MathSciNet: MR1401847
Digital Object Identifier: 10.1214/aos/1032526966

Primary: 62A15
Secondary: 60A05

Keywords: Cardinality , Coherence , consistent inference , diffuse probability , finite additivity , perfect probability , posterior Bayes rule , prediction , Sufficient statistic

Rights: Copyright © 1996 Institute of Mathematical Statistics

Vol.24 • No. 3 • June 1996
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