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On the Validity of the Markov Interpretation of Path Diagrams of Gaussian Structural Equations Systems with Correlated Errors
Author(s) -
Koster Jan T. A.
Publication year - 1999
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00157
Subject(s) - mathematics , markov chain , multivariate normal distribution , path (computing) , interpretation (philosophy) , gaussian , class (philosophy) , discrete mathematics , combinatorics , markov property , multivariate statistics , calculus (dental) , markov model , statistics , artificial intelligence , medicine , physics , dentistry , quantum mechanics , computer science , programming language
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”.