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Zbl 0964.62003
Nogales, Agustin G.; Oyola, José A.; Pérez, Paloma
On conditional independence and the relationship between sufficiency and invariance under the Bayesian point of view. (English)
[J] Stat. Probab. Lett. 46, No.1, 75-84 (2000). ISSN 0167-7152

The paper presents, from a Bayesian point of view, several results about conditional independence and about its role in analyzing the relations between concepts of sufficiency and concepts of invariance. Some of the given results are, in particular, related with the Bayesian translation of the ``Stein theorem'' [see {\it W.J. Hall}, {\it R.A. Wijsman} and {\it J.K. Ghosh}, Ann. Math. Stat. 36, 575-614 (1965; Zbl 0227.62007)], which gives sufficient conditions under which ${\cal A}_S\cap {\cal A}_I$ is sufficient for ${\cal A}_I$, where ${\cal A}_S$ is a sufficient $\sigma$-field and ${\cal A}_I$ is the $\sigma$-field of all events, invariant under the action of a given group $G$.\par The paper starts with a brief review about concepts of sufficiency and invariance (both in the classic and Bayesian statistics settings) and ends with some further discussion about the Stein theorem. Some examples of the theory are provided.

MSC 2000:: *62A01 Foundational and philosophical topics
62B05 Sufficient statistics

Keywords: conditional independence; measurable space; sufficiency; invariance

Citations: Zbl 0227.62007

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