Bayesian Networks and Influence Diagrams: A Guide to by Uffe B. Kjærulff, Anders L. Madsen

By Uffe B. Kjærulff, Anders L. Madsen

Bayesian Networks and impression Diagrams: A consultant to development and research, moment Edition, offers a accomplished advisor for practitioners who desire to comprehend, build, and study clever structures for selection aid in accordance with probabilistic networks. This new version includes six new sections, as well as fully-updated examples, tables, figures, and a revised appendix. meant basically for practitioners, this ebook doesn't require refined mathematical abilities or deep knowing of the underlying concept and strategies nor does it speak about replacement applied sciences for reasoning lower than uncertainty. the idea and techniques offered are illustrated via greater than one hundred forty examples, and workouts are incorporated for the reader to ascertain his or her point of figuring out. The suggestions and strategies awarded for wisdom elicitation, version building and verification, modeling options and methods, studying types from info, and analyses of types have all been constructed and subtle at the foundation of diverse classes that the authors have held for practitioners around the world.

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Chapter 3 Probabilities As mentioned in Chap. 2, probabilistic networks have a qualitative aspect and a corresponding quantitative aspect, where the qualitative aspect is given by a graphical structure in the form of a DAG that represents the (conditional) dependence and independence properties of a joint probability distribution defined over a set of variables that are indexed by the vertices of the DAG. The fact that the structure of a probabilistic network can be characterized as a DAG derives from basic axioms of probability calculus leading to recursive factorization of a joint probability distribution into a product of lower-dimensional conditional probability distributions.

X; Y /. 6 (Balls in An Urn, page 42). X2 D red | X1 D red/ 2 1 10 9 1 , D 45 D etc. X1 D blue; X2 / 0 1 0 1 0 1 0 1 1 1 1 1 B 45 C B 15 C B 9 C B 5 C B C B C B C B C B 1 C B 1 C B1C B 3 C B B B B C C C C. DB CCB CCB CDB C B 15 C B 15 C B 6 C B 10 C @ 1 A @ 1 A @2A @ 1 A 9 6 9 2 That is, the probabilities of getting a red, a green, and a blue ball in the second draw are, respectively, 0:2, 0:3, and 0:5, given that we know nothing about the color of the first ball. 0:1111; 0:3333; 0:5556/; that is, once the color of the first ball is known, our belief about the color of the second changes.

Thus, contrary to serial and diverging connections, a converging connection will not transmit information if no evidence is available for the middle variable. This fact is illustrated in Fig. 8. Second, if evidence is available on Alarm, then information about the state of Burglary will provide an explanation for the evidence that was received about the state of Alarm and thus either confirm or disconfirm Earthquake as the cause of the evidence received for Alarm. The opposite, of course, also holds true.

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