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 direc...
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| Veröffentlicht in: | Scandinavian journal of statistics 1999-09, Vol.26 (3), p.413-431 |
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| container_title | Scandinavian journal of statistics |
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| creator | Koster, Jan T. A. |
| description | 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". |
| doi_str_mv | 10.1111/1467-9469.00157 |
| format | Article |
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A.</creatorcontrib><title>On the Validity of the Markov Interpretation of Path Diagrams of Gaussian Structural Equations Systems with Correlated Errors</title><title>Scandinavian journal of statistics</title><description>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. 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A.</creator><general>Blackwell Publishers Ltd</general><general>Blackwell Publishers</general><general>Blackwell</general><general>Danish Society for Theoretical Statistics</general><scope>BSCLL</scope><scope>IQODW</scope><scope>DKI</scope><scope>X2L</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>199909</creationdate><title>On the Validity of the Markov Interpretation of Path Diagrams of Gaussian Structural Equations Systems with Correlated Errors</title><author>Koster, Jan T. A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c4397-b45701044dced47b39d7b2a4ba35f746d63418121e736909804680c9387784e53</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1999</creationdate><topic>Covariance matrices</topic><topic>d-separation</topic><topic>Directed acyclic graphs</topic><topic>Exact sciences and technology</topic><topic>Gaussian equations system</topic><topic>graph</topic><topic>graphical model</topic><topic>Linear equations</topic><topic>linear structural equation model</topic><topic>Marginalization</topic><topic>Markov models</topic><topic>Markov processes</topic><topic>Markov property</topic><topic>Mathematical independent variables</topic><topic>Mathematics</topic><topic>path diagram</topic><topic>Probability and statistics</topic><topic>Probability distributions</topic><topic>Probability theory and stochastic processes</topic><topic>Sciences and techniques of general use</topic><topic>Statistical theories</topic><topic>Stochastic analysis</topic><topic>Structural equation models</topic><topic>Vertices</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Koster, Jan T. A.</creatorcontrib><collection>Istex</collection><collection>Pascal-Francis</collection><collection>RePEc IDEAS</collection><collection>RePEc</collection><collection>CrossRef</collection><jtitle>Scandinavian journal of statistics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Koster, Jan T. A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the Validity of the Markov Interpretation of Path Diagrams of Gaussian Structural Equations Systems with Correlated Errors</atitle><jtitle>Scandinavian journal of statistics</jtitle><date>1999-09</date><risdate>1999</risdate><volume>26</volume><issue>3</issue><spage>413</spage><epage>431</epage><pages>413-431</pages><issn>0303-6898</issn><eissn>1467-9469</eissn><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".</abstract><cop>Oxford, UK and Boston, USA</cop><pub>Blackwell Publishers Ltd</pub><doi>10.1111/1467-9469.00157</doi><tpages>19</tpages></addata></record> |
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| ispartof | Scandinavian journal of statistics, 1999-09, Vol.26 (3), p.413-431 |
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| language | eng |
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| source | Jstor Complete Legacy; RePEc; Wiley Online Library Journals Frontfile Complete; Business Source Complete; JSTOR Mathematics & Statistics |
| subjects | Covariance matrices d-separation Directed acyclic graphs Exact sciences and technology Gaussian equations system graph graphical model Linear equations linear structural equation model Marginalization Markov models Markov processes Markov property Mathematical independent variables Mathematics path diagram Probability and statistics Probability distributions Probability theory and stochastic processes Sciences and techniques of general use Statistical theories Stochastic analysis Structural equation models Vertices |
| title | On the Validity of the Markov Interpretation of Path Diagrams of Gaussian Structural Equations Systems with Correlated Errors |
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