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Foundations for Bayesian networks
, 2001
"... Bayesian networks are normally given one of two types of foundations: they are either treated purely formally as an abstract way of representing probability functions, or they are interpreted, with some causal interpretation given to the graph in a network and some standard interpretation of probabi ..."
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Cited by 11 (7 self)
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Bayesian networks are normally given one of two types of foundations: they are either treated purely formally as an abstract way of representing probability functions, or they are interpreted, with some causal interpretation given to the graph in a network and some standard interpretation of probability given to the probabilities specified in the network. In this chapter I argue that current foundations are problematic, and put forward new foundations which involve aspects of both the interpreted and the formal approaches. One standard approach is to interpret a Bayesian network objectively: the graph in a Bayesian network represents causality in the world and the specified probabilities are objective, empirical probabilities. Such an interpretation founders when the Bayesian network independence assumption (often called the causal Markov condition) fails to hold. In §2 I catalogue the occasions when the independence assumption fails, and show that such failures are pervasive. Next, in §3, I show that even where the independence assumption does hold objectively, an agent’s causal knowledge is unlikely to satisfy the assumption with respect to her subjective probabilities, and that slight differences between an agent’s subjective Bayesian network and an objective Bayesian network can lead to large differences between probability distributions determined by these networks. To overcome these difficulties I put forward logical Bayesian foundations in §5. I show that if the graph and probability specification in a Bayesian network are thought of as an agent’s background knowledge, then the agent is most rational if she adopts the probability distribution determined by the
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, 2002
"... This URL will also contain a link to the author’s home page. The publishers will keep this article online on the Internet (or its possible replacement network in the future) for a period of 25 years from the date of publication, barring exceptional circumstances as described separately. The online ..."
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This URL will also contain a link to the author’s home page. The publishers will keep this article online on the Internet (or its possible replacement network in the future) for a period of 25 years from the date of publication, barring exceptional circumstances as described separately. The online availability of the article implies a permanent permission for anyone to read the article online, to print out single copies of it, and to use it unchanged for any noncommercial research and educational purpose, including making copies for classroom use. This permission can not be revoked by subsequent transfers of copyright. All other uses of the article are conditional on the consent of the copyright owner. The publication of the article on the date stated above included also the production of a limited number of copies on paper, which were archived in Swedish university libraries like all other written works published in Sweden. The publisher has taken technical and administrative measures to assure that the online version of the article will be permanently accessible using the URL stated above, unchanged, and permanently equal to the archived printed copies at least until the expiration of the publication period. For additional information about the Linköping University Electronic Press and its procedures for publication and for assurance of document integrity, please refer to its WWW home page: