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On the existence of inferences which are consistent with a given model. (English) Zbl 0866.62001
Summary: 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 D. A. Lane and W. D. Sudderth [ibid. 11, 114-120 (1983; Zbl 0555.62008)]. 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.

62A01 Foundations and philosophical topics in statistics
Full Text: DOI
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