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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 selection making lower than uncertainty. As modeling languages they permit 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 comprises trust updating, discovering the main possible cause of the saw facts, detecting conflicts within the proof entered into the community, deciding upon optimum recommendations, studying for relevance, and acting sensitivity analysis.

The e-book introduces probabilistic graphical types and determination graphs, together with Bayesian networks and impact diagrams. The reader is brought to the 2 forms of frameworks via examples and routines, which additionally train the reader on easy methods to construct those types.

The booklet is a brand new version of Bayesian Networks and choice Graphs through Finn V. Jensen. the recent version is dependent into elements. the 1st half makes a speciality of probabilistic graphical types. in comparison with the former publication, the recent version additionally encompasses a thorough description of modern extensions to the Bayesian community modeling language, advances in specific and approximate trust updating algorithms, and techniques for studying either the constitution and the parameters of a Bayesian community. the second one half offers with determination graphs, and likewise to the frameworks defined within the earlier version, it additionally introduces Markov determination procedures and partly ordered selection difficulties. The authors additionally

    • provide a well-founded functional advent to Bayesian networks, object-oriented Bayesian networks, determination bushes, impression diagrams (and versions hereof), and Markov determination processes.
    • give functional recommendation at the building of Bayesian networks, choice bushes, and impression diagrams from area knowledge.
    • <

    • give a number of examples and workouts exploiting computers for facing Bayesian networks and determination graphs.
    • present a radical creation to cutting-edge answer and research algorithms.

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

Finn V. Jensen is a professor on the division of computing device technological know-how at Aalborg collage, Denmark.

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

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Extra info for Bayesian Networks and Decision Graphs: February 8, 2007

Sample text

Next, we get the information that FM = 21 , and the context for calculation is limited to the part with FM = 12 and St = no. 4. 4. P (Fu, SP, St = no, FM = 12 ). 804). The probability of SP = yes increased by observing FM = 12 , so the calculus did catch the explaining away effect. 3 Inserting Evidence Bayesian networks are used for calculating new probabilities when you get new information. The information so far has been of the type “A = a,” where A is 40 2 Causal and Bayesian Networks a variable and a is a state of A.

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. Since the probability is zero for any particular outcome, the probability distribution is assigned to subsets of the unit square.

An−1 ) = P (An−1 | A1 , . . , An−2 )P (A1 , . . , An−2 ), .. P (A1 , A2 ) = P (A2 | A1 )P (A1 ). 1 (The chain rule for Bayesian networks). Let BN be a Bayesian network over U = {A1 , . . , An }. 3 Bayesian Networks 37 where pa(Ai ) are the parents of Ai in BN , and P (U) reflects the properties of BN . Proof. First we should show that P (U) is indeed a probability distribution. That is, we need to show that Axioms 1–3 hold. 15). Next we prove that the specification of BN is consistent, so that P (U) reflects the properties of BN .

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