{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:46:07Z","timestamp":1753886767164,"version":"3.41.2"},"reference-count":14,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2010,12,20]],"date-time":"2010-12-20T00:00:00Z","timestamp":1292803200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2011,1]]},"abstract":"<jats:p>Bayesian Networks are graphic probabilistic models through\nwhich we can acquire, capitalize on, and exploit knowledge. they are becoming\nan important tool for research and applications in artificial intelligence\nand many other fields in the last decade. This paper presents\nBayesian networks and discusses the inference problem in such models. It\nproposes a statement of the problem and the proposed method to compute\nprobability distributions. It also uses D\u2010separation for simplifying\nthe computation of probabilities in Bayesian networks. Given a Bayesian\nnetwork over a family <jats:italic>I<\/jats:italic> of random variables, this paper presents a result\non the computation of the probability distribution of a subset <jats:italic>S<\/jats:italic> of <jats:italic>I<\/jats:italic>\nusing separately a computation algorithm and D\u2010separation properties. \nIt also shows the uniqueness of the obtained result.<\/jats:p>","DOI":"10.1155\/2011\/845398","type":"journal-article","created":{"date-parts":[[2010,12,20]],"date-time":"2010-12-20T19:37:05Z","timestamp":1292873825000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Uniqueness of the Level Two Bayesian Network Representing a Probability Distribution"],"prefix":"10.1155","volume":"2011","author":[{"given":"Linda","family":"Smail","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2010,12,20]]},"reference":[{"volume-title":"An Introduction to Bayesian Networks","year":"1999","author":"Jensen F. 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