A note on marginal and conditional independence

Nicola Loperfido

Some statistical models imply that two random vectors are marginally independent as well as being conditionally independent with respect to another random vector. When the joint distributions of the vectors is normal, Canonical Correlation Analysis may lead to relevant simplifications of the dependence structure. A similar application can be found in elliptical models, where linear independence does not imply statistical independence. Implications for Bayes analysis of the general linear model are discussed.

Mots clés: Bayes linear analysis; Canonical Correlation Analysis; Elliptical distributions; Sylvester law of nullity; Unrelated parameters

Domaines: Bio-informatique [q-bio.QM]; Bio-Informatique, Biologie Systémique [q-bio.QM]

Nicola Loperfido. A note on marginal and conditional independence. Statistics and Probability Letters, 2010, 80 (23-24), pp.1695. ⟨10.1016/j.spl.2010.07.007⟩. ⟨hal-00691791⟩