On Gaussian conditional independence structures
The simultaneous occurrence of conditional independences among subvectors of a regular Gaussian vector is examined. All configurations of the conditional independences within four jointly regular Gaussian variables are found and completely characterized in terms of implications involving conditional independence statements. The statements induced by the separation in any simple graph are shown to correspond to such a configuration within a regular Gaussian vector.
conditional independence multivariate gaussian distribution positive definite matrices determinants principal minors probabilistic representability semi-graphoids separation graphoids gaussoids covariance selection models markov perfectness