{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T05:57:07Z","timestamp":1791525427122,"version":"4.3.4"},"reference-count":33,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2014,5,30]],"date-time":"2014-05-30T00:00:00Z","timestamp":1401408000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100001711","name":"Swiss National Science Foundation","doi-asserted-by":"publisher","award":["20PA20E-134493\/1"],"award-info":[{"award-number":["20PA20E-134493\/1"]}],"id":[{"id":"10.13039\/501100001711","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015,1,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>In many applications we have both observational and (randomized) interventional data. We propose a Gaussian likelihood framework for joint modelling of such different data types, based on global parameters consisting of a directed acyclic graph and corresponding edge weights and error variances. Thanks to the global nature of the parameters, maximum likelihood estimation is reasonable with only one or few data points per intervention. We prove consistency of the Bayesian information criterion for estimating the interventional Markov equivalence class of directed acyclic graphs which is smaller than the observational analogue owing to increased partial identifiability from interventional data. Such an improvement in identifiability has immediate implications for tighter bounds for inferring causal effects. Besides methodology and theoretical derivations, we present empirical results from real and simulated data.<\/jats:p>","DOI":"10.1111\/rssb.12071","type":"journal-article","created":{"date-parts":[[2014,5,30]],"date-time":"2014-05-30T05:29:04Z","timestamp":1401427744000},"page":"291-318","source":"Crossref","is-referenced-by-count":40,"title":["Jointly Interventional and Observational Data: Estimation of Interventional Markov Equivalence Classes of Directed Acyclic Graphs"],"prefix":"10.1093","volume":"77","author":[{"given":"Alain","family":"Hauser","sequence":"first","affiliation":[{"name":"University of Bern, and Swiss Institute of Bioinformatics , Lausanne , Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter","family":"B\u00fchlmann","sequence":"additional","affiliation":[{"name":"Eidgen\u00f6ssiche Technische Hochschule , Z\u00fcrich , Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2014,5,30]]},"reference":[{"key":"2023022002192013500_rssb12071-cit-0001","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1214\/aos\/1031833662","article-title":"A characterization of Markov equivalence classes for acyclic digraphs","volume":"25","author":"Andersson","year":"1997","journal-title":"Ann. 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