We try to show that Discriminant Analysis can be considered as a branch of Statistical Decision Theory when viewed from a Bayesian approach. First we present the necessary measure theory results, next we briefly outline the foundations of Bayesian Inference before developing Discriminant Analysis as an application of Bayesian Estimation. Our approach renders Discriminant Analysis more flexible since it gives the possibility of classing an element as belonging to a group of populations. This possibility arises from the introduction of the concept of regions of controled posterior risk.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1083,
author = {Sandra Saraiva Ferreira and D\'ario Ferreira and Jo\~ao Tiago Mexia},
title = {Cross additivity - an application},
journal = {Discussiones Mathematicae Probability and Statistics},
volume = {26},
year = {2006},
pages = {207-219},
zbl = {1128.62073},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1083}
}
Sandra Saraiva Ferreira; Dário Ferreira; João Tiago Mexia. Cross additivity - an application. Discussiones Mathematicae Probability and Statistics, Tome 26 (2006) pp. 207-219. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1083/
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[002] [3] S.F. Saraiva, Inference for Orthogonal Models with Segregation, PhD Thesis, UBI - Covilhã 2006.