Geodesic
Cross additivity - an application
Discussiones Mathematicae. Probability and Statistics, Tome 26 (2006) no. 2, pp. 207-219.

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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.
Keywords: cross nested designs, cross additivity, variance components, UMVUE 
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Ferreira, Sandra; Ferreira, Dário; Mexia, João. Cross additivity - an application. Discussiones Mathematicae. Probability and Statistics, Tome 26 (2006) no. 2, pp. 207-219. http://geodesic.mathdoc.fr/item/DMPS_2006_26_2_a6/

[1] M. Fonseca, J.T. Mexia and R. Zmyślony, Estimating and testing of variance components: an application to a grapevine experiment, Biometrical Letters 40 (1) (2003), 1-7.

[2] J.T. Mexia, Introduction to Linear Statistical Inference, Center of Studies of Applied Mathematics, Lusófonas Editions - Lisboa 1995.

[3] S.F. Saraiva, Inference for Orthogonal Models with Segregation, PhD Thesis, UBI - Covilhã 2006.