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{1176345011,
author = {Dawid, A. Philip},
title = {Conditional Independence for Statistical Operations},
journal = {Ann. Statist.},
volume = {8},
number = {1},
year = {1980},
pages = { 598-617},
language = {en},
url = {http://dml.mathdoc.fr/item/1176345011}
}
Dawid, A. Philip. Conditional Independence for Statistical Operations. Ann. Statist., Tome 8 (1980) no. 1, pp. 598-617. http://gdmltest.u-ga.fr/item/1176345011/