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However, the apparent simplicity of chain graphs belies the subtlety of the conditional independence hypotheses that they represent. There are many simple and apparently plausible, but ultimately fallacious, interpretations of chain graphs that are often invoked, implicitly or explicitly. These interpretations also lead to flawed methods for applying background knowledge to model selection. We present a valid interpretation by showing how the distribution corresponding to a chain graph may be generated from the equilibrium distributions of dynamic models with feed-back. These dynamic interpretations lead to a simple theory of intervention, extending the theory developed for directed acyclic graphs. Finally, we contrast chain graph models under this interpretation with simultaneous equation models which have traditionally been used to model feed-back in econometrics.<\/jats:p>","DOI":"10.1111\/1467-9868.00340","type":"journal-article","created":{"date-parts":[[2003,3,12]],"date-time":"2003-03-12T19:37:22Z","timestamp":1047497842000},"page":"321-348","source":"Crossref","is-referenced-by-count":139,"title":["Chain Graph Models and their Causal Interpretations"],"prefix":"10.1093","volume":"64","author":[{"given":"Steffen L.","family":"Lauritzen","sequence":"first","affiliation":[{"name":"Aalborg University , Denmark"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Thomas S.","family":"Richardson","sequence":"additional","affiliation":[{"name":"University of Washington , Seattle , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2002,8,12]]},"reference":[{"key":"2023040109112337000_","volume-title":"An alternative Markov property for chain graphs","author":"Andersson","year":"1996"},{"key":"2023040109112337000_","first-page":"505","article-title":"A characterization of Markov equivalence classes for acyclic digraphs","volume":"25","year":"1997","journal-title":"Ann. 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