The Annals of Statistics

Conditional Independence for Statistical Operations

A. Philip Dawid

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Abstract

A general calculus of conditional independence is developed, suitable for application to a wide range of statistical concepts such as sufficiency, parameter-identification, adequacy and ancillarity. A vehicle for this theory is the statistical operation, a structure-preserving map between statistical spaces. Concepts such as completeness and identifiability of mixtures arise naturally and play an important part. Some general theorems are exemplified by applications to ancillarity, including a study of a Bayesian definition of ancillarity in the presence of nuisance parameters.

Article information

Source
Ann. Statist., Volume 8, Number 3 (1980), 598-617.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345011

Digital Object Identifier
doi:10.1214/aos/1176345011

Mathematical Reviews number (MathSciNet)
MR568723

Zentralblatt MATH identifier
0434.62006

JSTOR
links.jstor.org

Subjects
Primary: 62A99: None of the above, but in this section
Secondary: 60A05: Axioms; other general questions

Keywords
Statistical operation conditional independence sufficiency ancillarity adequacy completeness

Citation

Dawid, A. Philip. Conditional Independence for Statistical Operations. Ann. Statist. 8 (1980), no. 3, 598--617. doi:10.1214/aos/1176345011. https://projecteuclid.org/euclid.aos/1176345011


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