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

Jan T. A. Koster

Scandinavian Journal of Statistics, 1999, vol. 26, issue 3, 413-431

Abstract: 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”.

Date: 1999
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