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

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

Probabilistic graphical versions and choice graphs are strong modeling instruments for reasoning and choice making lower than uncertainty. As modeling languages they enable a normal specification of challenge domain names with inherent uncertainty, and from a computational standpoint they help effective algorithms for computerized building and question answering. This comprises trust updating, discovering the main possible reason behind the saw facts, detecting conflicts within the proof entered into the community, settling on optimum options, studying for relevance, and appearing sensitivity analysis.

The ebook introduces probabilistic graphical versions and selection graphs, together with Bayesian networks and impact diagrams. The reader is brought to the 2 sorts of frameworks via examples and workouts, which additionally train the reader on the right way to construct those types.

The e-book is a brand new version of Bayesian Networks and choice Graphs through Finn V. Jensen. the hot variation is dependent into elements. the 1st half specializes in probabilistic graphical versions. in comparison with the former booklet, the hot variation additionally contains a thorough description of modern extensions to the Bayesian community modeling language, advances in detailed and approximate trust updating algorithms, and strategies for studying either the constitution and the parameters of a Bayesian community. the second one half offers with determination graphs, and also to the frameworks defined within the prior version, it additionally introduces Markov selection approaches and partly ordered choice difficulties. The authors additionally

    • provide a well-founded sensible creation to Bayesian networks, object-oriented Bayesian networks, determination bushes, impression diagrams (and editions hereof), and Markov choice processes.
    • give sensible suggestion at the development of Bayesian networks, determination timber, and effect diagrams from area knowledge.
    • <

    • give a number of examples and routines exploiting desktops for facing Bayesian networks and choice graphs.
    • present an intensive creation to cutting-edge answer and research algorithms.

The ebook is meant as a textbook, however it is usually 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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Example text

The hypothesis events detected are then grouped into sets of mutually exclusive and exhaustive events to form hypothesis variable. The next thing to have in mind is that in order to come up with a certainty estimate, we should provide some information channels, and the task is to identify the types of achievable information that may reveal something about the hypothesis variables.

We let R be a variable representing the roll of the red die, having a set of states {r1, r2, r3, r4, r5, r6}, and B be a variable representing the roll of the blue die (states {b1, b2, b3, b4, b5, b6}). Assume that the red die is fair so that P (R = r1) = · · · = P (R = r6) = 61 , and that the variable for the blue 1 die has probabilities P (B = b1) = P (B = b2) = P (B = b3) = 12 and 1 P (B = b4) = P (B = b5) = P (B = b6) = 4 . Give an example of a sample space for an experiment consisting of throwing both the red and the blue die.

The test has the above characteristics. Experience says that 20% of the drivers under suspicion do in fact drive with too much alcohol in their blood. A suspicious driver has a positive blood test. What is the probability that the driver is guilty of driving under the influence of alcohol? (ii) The police block a road, take blood samples of all drivers, and use the same test. It is estimated that one out of 1,000 drivers have too much alcohol in their blood. A driver has a positive test result. What is the probability that the driver is guilty of driving under the influence of alcohol?

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