Download Bayesian Networks and Decision Graphs: February 8, 2007 by Finn V. Jensen, Thomas D. Nielsen (auth.) PDF

By Finn V. Jensen, Thomas D. Nielsen (auth.)

Probabilistic graphical versions and selection graphs are robust modeling instruments for reasoning and determination making less than uncertainty. As modeling languages they enable a common specification of challenge domain names with inherent uncertainty, and from a computational standpoint they aid effective algorithms for automated building and question answering. This contains trust updating, discovering the main possible cause of the saw proof, detecting conflicts within the proof entered into the community, deciding upon optimum ideas, interpreting for relevance, and acting sensitivity analysis.

The publication introduces probabilistic graphical versions and choice graphs, together with Bayesian networks and impression diagrams. The reader is brought to the 2 forms of frameworks via examples and workouts, which additionally teach the reader on the best way to construct those types.

The e-book is a brand new version of Bayesian Networks and choice Graphs by way of Finn V. Jensen. the recent version is dependent into components. the 1st half makes a speciality of probabilistic graphical versions. in comparison with the former publication, the hot variation additionally features a thorough description of contemporary extensions to the Bayesian community modeling language, advances in precise and approximate trust updating algorithms, and techniques for studying either the constitution and the parameters of a Bayesian community. the second one half bargains with selection graphs, and also to the frameworks defined within the earlier variation, it additionally introduces Markov choice procedures and partly ordered selection difficulties. The authors additionally

    • provide a well-founded useful advent to Bayesian networks, object-oriented Bayesian networks, determination timber, impression diagrams (and variations hereof), and Markov choice processes.
    • give useful recommendation at the building of Bayesian networks, choice timber, and impact diagrams from area knowledge.
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    • give numerous examples and routines exploiting computers for facing Bayesian networks and determination graphs.
    • present a radical advent to state of the art resolution and research algorithms.

The booklet is meant as a textbook, however it is additionally used for self-study and as a reference book.

Finn V. Jensen is a professor on the division of laptop technology at Aalborg collage, Denmark.

Thomas D. Nielsen is an affiliate professor on the similar department.

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The mean value is also called the expected value. A measure of how much a random variable varies between its values is the variance, σ 2 . It is defined as the mean of the square of the difference between value and mean: σ 2 (V ) = (V (s) − μ(V ))2 P (s). 7) s∈S For the example above we have σ 2 = 3(−1 − 0)2 1 1 + 3(1 − 0)2 = 1. 1 Continuous Distributions Consider an experiment, where an arrow is thrown at the [0, 1] × [0, 1] square. The possible outcomes are the points (x, y) in the unit square.

0, xi , 0, . . , 0, xj , 0, . . , 0). Note that P (e), the prior probability of e, is obtained by marginalizing A out of P (A, e). Note also that P (A, e) is the result of multiplying P (A) by (0, . . , 0, 1, 0, . . , 0, 1, 0, . . , 0), where the 1’s are at the i’th and j’th places. 4. Let A be a variable with n states. A finding on A is an ndimensional table of zeros and ones. To distinguish between the statement e, “A is in either state i or j,” and the corresponding 0/1-finding vector, we sometimes use the boldface notation e for the finding.

For the second case, we first note that P (An | B, C) = P (An | B, C, pa(An ))P (pa(An ) | B, C). pa(An ) Now, if An and B are d-separated given C, then pa(An ) and B are also dseparated given C, and since An is not involved, we have P (pa(An ) | B, C) = 38 2 Causal and Bayesian Networks P (pa(An ) | C). So we need to prove only that P (An | B, C, pa(An )) = P (An | pa(An )). Using the fundamental rule and the chain rule, we get P (An | B, C, pa(An )) = = P (An , B, C, pa(An )) = P (B, C, pa(An )) U \{An ,B,C,pa(An )} U \{B,C,pa(An )} = = n i=1 n i=1 U \{An ,B,C,pa(An )} U \{B,C,pa(An )} P (U) P (U) P (Ai | pa(Ai )) P (Ai | pa(Ai )) n−1 U \{An ,B,C,pa(An )} i=1 P (Ai | pa(Ai )) n−1 U \{An ,B,C,pa(An )} An P (An | pa(An )) i=1 P (Ai | pa(Ai )) n−1 P (An | pa(An )) U \{An ,B,C,pa(An )} i=1 P (Ai | pa(Ai )) n−1 U \{An ,B,C,pa(An )} i=1 P (Ai | pa(Ai ))1 P (An | pa(An )) = P (An | pa(An )).

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