{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T17:52:25Z","timestamp":1772041945507,"version":"3.50.1"},"reference-count":35,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2018,12,14]],"date-time":"2018-12-14T00:00:00Z","timestamp":1544745600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper combines Bayesian networks (BN) and information theory to model the likelihood of severe loss of separation (LOS) near accidents, which are considered mid-air collision (MAC) precursors. BN is used to analyze LOS contributing factors and the multi-dependent relationship of causal factors, while Information Theory is used to identify the LOS precursors that provide the most information. The combination of the two techniques allows us to use data on LOS causes and precursors to define warning scenarios that could forecast a major LOS with severity A or a near accident, and consequently the likelihood of a MAC. The methodology is illustrated with a case study that encompasses the analysis of LOS that have taken place within the Spanish airspace during a period of four years.<\/jats:p>","DOI":"10.3390\/e20120969","type":"journal-article","created":{"date-parts":[[2018,12,14]],"date-time":"2018-12-14T04:44:42Z","timestamp":1544762682000},"page":"969","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Application of Bayesian Networks and Information Theory to Estimate the Occurrence of Mid-Air Collisions Based on Accident Precursors"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6639-6819","authenticated-orcid":false,"given":"Rosa Mar\u00eda","family":"Arnaldo Vald\u00e9s","sequence":"first","affiliation":[{"name":"Department of Sistemas Aeroespaciales, Transporte A\u00e9reo y Aeropuertos, School of Aerospace Engineering, Universidad Polit\u00e9cnica de Madrid (UPM), Plaza Cardenal Cisneros n3, 28040 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8701-9059","authenticated-orcid":false,"given":"Schon Z.Y.","family":"Liang Cheng","sequence":"additional","affiliation":[{"name":"Department of Sistemas Aeroespaciales, Transporte A\u00e9reo y Aeropuertos, School of Aerospace Engineering, Universidad Polit\u00e9cnica de Madrid (UPM), Plaza Cardenal Cisneros n3, 28040 Madrid, Spain"},{"name":"Aeronautic, Space &amp; Defence Division, ALTRAN Innovation S.L., Calle Campezo 128022 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0961-2188","authenticated-orcid":false,"given":"Victor Fernando","family":"G\u00f3mez Comendador","sequence":"additional","affiliation":[{"name":"Department of Sistemas Aeroespaciales, Transporte A\u00e9reo y Aeropuertos, School of Aerospace Engineering, Universidad Polit\u00e9cnica de Madrid (UPM), Plaza Cardenal Cisneros n3, 28040 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7500-4706","authenticated-orcid":false,"given":"Francisco Javier","family":"S\u00e1ez Nieto","sequence":"additional","affiliation":[{"name":"Centre for Aeronautics, School of Aerospace, Transport and Manufacturing, Cranfield University, Cranfield MK43 OAL, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,12,14]]},"reference":[{"key":"ref_1","unstructured":"(2018, December 01). 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