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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.

##### MSC:
 62A01 Foundations and philosophical topics in statistics
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##### References:
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