# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
On conditional independence and the relationship between sufficiency and invariance under the Bayesian point of view. (English) Zbl 0964.62003

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 W.J. Hall, R.A. Wijsman and J.K. Ghosh, Ann. Math. Stat. 36, 575-614 (1965; Zbl 0227.62007)], which gives sufficient conditions under which ${𝒜}_{S}\cap {𝒜}_{I}$ is sufficient for ${𝒜}_{I}$, where ${𝒜}_{S}$ is a sufficient $\sigma$-field and ${𝒜}_{I}$ is the $\sigma$-field of all events, invariant under the action of a given group $G$.

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:
 62A01 Foundations and philosophical topics in statistics 62B05 Sufficient statistics and fields