{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,19]],"date-time":"2026-04-19T00:45:16Z","timestamp":1776559516194,"version":"3.51.2"},"reference-count":64,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2020,7,31]],"date-time":"2020-07-31T00:00:00Z","timestamp":1596153600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["AGS-1637450"],"award-info":[{"award-number":["AGS-1637450"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CCF-0939370"],"award-info":[{"award-number":["CCF-0939370"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["IIS-1522125"],"award-info":[{"award-number":["IIS-1522125"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100014036","name":"Multidisciplinary University Research Initiative","doi-asserted-by":"publisher","award":["ARO-W911NF-15-1-0479"],"award-info":[{"award-number":["ARO-W911NF-15-1-0479"]}],"id":[{"id":"10.13039\/100014036","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["1R01MH110514"],"award-info":[{"award-number":["1R01MH110514"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Information theoretic (IT) approaches to quantifying causal influences have experienced some popularity in the literature, in both theoretical and applied (e.g., neuroscience and climate science) domains. While these causal measures are desirable in that they are model agnostic and can capture non-linear interactions, they are fundamentally different from common statistical notions of causal influence in that they (1) compare distributions over the effect rather than values of the effect and (2) are defined with respect to random variables representing a cause rather than specific values of a cause. We here present IT measures of direct, indirect, and total causal effects. The proposed measures are unlike existing IT techniques in that they enable measuring causal effects that are defined with respect to specific values of a cause while still offering the flexibility and general applicability of IT techniques. We provide an identifiability result and demonstrate application of the proposed measures in estimating the causal effect of the El Ni\u00f1o\u2013Southern Oscillation on temperature anomalies in the North American Pacific Northwest.<\/jats:p>","DOI":"10.3390\/e22080854","type":"journal-article","created":{"date-parts":[[2020,8,3]],"date-time":"2020-08-03T03:16:46Z","timestamp":1596424606000},"page":"854","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Direct and Indirect Effects\u2014An Information Theoretic Perspective"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4188-9614","authenticated-orcid":false,"given":"Gabriel","family":"Schamberg","sequence":"first","affiliation":[{"name":"Picower Institute for Memory and Learning, Massachusetts Institute of Technology, Cambridge, MA 02139, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0472-7069","authenticated-orcid":false,"given":"William","family":"Chapman","sequence":"additional","affiliation":[{"name":"Scripps Institution of Oceanography, La Jolla, CA 92037, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3676-1325","authenticated-orcid":false,"given":"Shang-Ping","family":"Xie","sequence":"additional","affiliation":[{"name":"Scripps Institution of Oceanography, La Jolla, CA 92037, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Todd","family":"Coleman","sequence":"additional","affiliation":[{"name":"Department of Bioengineering, University of California, La Jolla, CA 92093, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,7,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1214\/09-SS057","article-title":"Causal inference in statistics: An overview","volume":"3","author":"Pearl","year":"2009","journal-title":"Stat. 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