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By Uffe B. Kjærulff, Anders L. Madsen

Bayesian Networks and impression Diagrams: A advisor to development and research, moment Edition, offers a accomplished advisor for practitioners who desire to comprehend, build, and learn clever structures for selection aid according to probabilistic networks. This new version comprises six new sections, as well as fully-updated examples, tables, figures, and a revised appendix. meant basically for practitioners, this booklet doesn't require subtle mathematical talents or deep figuring out of the underlying idea and techniques nor does it talk about substitute applied sciences for reasoning below uncertainty. the idea and techniques provided are illustrated via greater than one hundred forty examples, and workouts are incorporated for the reader to ascertain his or her point of realizing. The thoughts and strategies awarded for wisdom elicitation, version development and verification, modeling innovations and tips, studying types from information, and analyses of versions have all been built and subtle at the foundation of various classes that the authors have held for practitioners world wide.

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Extra resources for Bayesian Networks and Influence Diagrams: A Guide to Construction and Analysis

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7 (d-Separation). 4 to determine if, for example, variables C and G are d-separated in the DAG in Fig. 13; that is, are C and G independent when no evidence about any of the variables is available? First, we find that there is a diverging connection C ← A → D allowing transmission of information from C to D via A. Second, there is a serial connection A → D → G allowing transmission of information from A to G via D. , they are d-connected). C and E, on the other hand, are d-separated since each path from C to E contains a converging connection, and since no evidence is available, each such connection will not allow transmission of information.

3, we show that for any joint probability distribution that factorizes according to a DAG, G (see Chap. 3 for a definition), independence statements involving variables Xu and Xv (again, see Chap. 3 for a definition) are equivalent to similar statements about d-separation of vertices u and v in G. Thus, the d-separation criterion may be used to answer queries of the kind “are X and Y independent given Z” (in a probabilistic sense) or, more generally, queries of the kind “is information about X irrelevant for our belief about the state of Y given information about Z,” where X and Y are individual variables and Z is either the empty set of variables or an individual variable.

Now, if information is received about the state of either Alarm or Radio news, then this information is not going to change our belief about the state of Earthquake, and consequently, we are not going to update our belief about the other, yet unobserved, variable. Again, this result is similar to the case for serial connections and is illustrated in Fig. 7. 2 (Diverging Connection). Information may be transmitted through a diverging connection X ← Y → Z unless the state of Y is known. 5 Flow of Information in Causal Networks Burglary 29 Earthquake Alarm Fig.

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