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Download PDF by Richard E. Neapolitan: Learning Bayesian networks

By Richard E. Neapolitan

ISBN-10: 0130125342

ISBN-13: 9780130125347

For classes in Bayesian Networks or complex Networking targeting Bayesian networks present in departments of desktop technological know-how, computing device Engineering and electric Engineering. additionally acceptable as a supplementary textual content in classes on professional platforms, laptop studying, and synthetic Intelligence the place the subject of Bayesian Networks is roofed. This publication offers an obtainable and unified dialogue of Bayesian networks. It comprises discussions of themes regarding the parts of synthetic intelligence, professional platforms and selection research, the fields within which Bayesian networks are usually utilized. the writer discusses either equipment for doing inference in Bayesian networks and impact diagrams. The e-book additionally covers the Bayesian process for studying the values of discrete and non-stop parameters. either the Bayesian and constraint-based tools for studying constitution are mentioned intimately.

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Example text

Something may seem amiss to you. 3 (a), then (P, G) satisfies the Markov condition. 4 to conclude we need only determine the conditional distributions of the variables for that DAG to find any value in the joint distribution. 27. 2, in application we do not ordinarily specify an underlying sample space and probability function from which we can compute conditional distributions. Rather we identify random variables and values in conditional distributions directly. 3. LARGE INSTANCES / BAYESIAN NETWORKS 37 yes), P (LungCancer = present|SmokingHistory = yes), and P (ChestXray = positive| LungCancer = present).

Instead, we identify random variables directly, and we determine probabilistic relationships among the random variables. The conditional probabilities of interest are often not the ones we are able to judge directly. We discuss next the meaning of random variables and probabilities in Bayesian applications and how they are identified directly. After that, we show how a joint probability distribution can be determined without first specifying a sample space. Finally, we show a useful application of Bayes’ Theorem.

Xn , let pai be the subset of these values containing the values of Xi ’s parents. We need show that whenever P (pai ) 6= 0 for 1 ≤ i ≤ n, P (xn , xn−1 , . . x1 ) = P (xn |pan )P (xn−1 |pan−1 ) · · · P (x1 |pa1 ). We show this using induction on the number of variables in the network. Assume, for some combination of values of the xi ’s, that P (pai ) 6= 0 for 1 ≤ i ≤ n. induction base: Since PA1 is empty, P (x1 ) = P (x1 |pa1 ). induction hypothesis: Suppose for this combination of values of the xi ’s that P (xi , xi−1 , .

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