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Berti, Patrizia; Rigo, Pietro

On the existence of inferences which are consistent with a given model. (English) Zbl 0866.62001

Ann. Stat. 24, No. 3, 1235-1249 (1996).
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.

Cited in 4 Documents

MSC:

62A01 Foundations and philosophical topics in statistics

Keywords:

Bayesian sufficiency; cardinality; coherence; consistent inference; diffuse probability; perfect probability; posterior Bayes rule; prediction; sigma-additive statistical model; finitely additive prior; consistency

Citations:

Zbl 0555.62008
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Full Text: DOI

References:

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