On the Validity of the Markov Interpretation of Path Diagrams of Gaussian Structural Equations Systems with Correlated Errors

Pearl's d-separation concept and the ensuing Markov property is applied to graphs which may have, between each two different vertices i and j, any subset of {i → j, i ← j, i ↔ j} as edges. The class of graphs so obtained is closed under marginalization. Furthermore, the approach permits a direct proof of this theorem: "The distribution of a multivariate normal random vector satisfying a system of linear simultaneous equations is Markov w.r.t. the path diagram of the linear system".