{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T11:43:00Z","timestamp":1753875780854,"version":"3.41.2"},"reference-count":38,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2024,8,21]],"date-time":"2024-08-21T00:00:00Z","timestamp":1724198400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,1,16]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Causal intervention is an essential tool in causal inference. It is axiomatized under the rules of do-calculus in the case of structure causal models. We provide simple axiomatizations for families of probability distributions to be different types of interventional distributions. Our axiomatizations neatly lead to a simple and clear theory of causality that has several advantages: it does not need to make use of any modelling assumptions such as those imposed by structural causal models; it relies only on interventions on single variables; it includes most cases with latent variables and causal cycles; and, more importantly, it does not assume the existence of an underlying true causal graph as we do not take it as the primitive object; moreover, a causal graph is derived as a by-product of our theory. We show that, under our axiomatizations, the intervened distributions are Markovian to the defined intervened causal graphs, and an observed joint probability distribution is Markovian to the obtained causal graph; these results are consistent with the case of structural causal models, and as a result, the existing theory of causal inference applies. We also show that a large class of natural structural causal models satisfy the theory presented here. The aim of this paper is axiomatization of interventional families, which is subtly different from causal modelling.<\/jats:p>","DOI":"10.1093\/biomet\/asae043","type":"journal-article","created":{"date-parts":[[2024,8,21]],"date-time":"2024-08-21T23:01:47Z","timestamp":1724281307000},"source":"Crossref","is-referenced-by-count":0,"title":["Axiomatization of interventional probability distributions"],"prefix":"10.1093","volume":"112","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7314-744X","authenticated-orcid":false,"given":"Kayvan","family":"Sadeghi","sequence":"first","affiliation":[{"name":"Department of Statistical Science, University College London , Gower Street , London, WC1E 6BT,","place":["UK"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Terry","family":"Soo","sequence":"additional","affiliation":[{"name":"Department of Statistical Science, University College London , Gower Street , London, WC1E 6BT,","place":["UK"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2024,8,21]]},"reference":[{"volume-title":"Local Characterizations of Causal Bayesian Networks","year":"2011","author":"Bareinboim","key":"2025012017232224500_asae043-B1"},{"key":"2025012017232224500_asae043-B2","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1145\/3501714.3501743","volume-title":"Probabilistic and Causal Inference: The Works of Judea Pearl","author":"Bareinboim","year":"2022","edition":"1st ed."},{"key":"2025012017232224500_asae043-B3","doi-asserted-by":"crossref","first-page":"2885","DOI":"10.1214\/21-AOS2064","article-title":"Foundations of structural causal models with cycles and latent variables","volume":"49","author":"Bongers","year":"2021","journal-title":"Ann. 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