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 determination graphs are strong modeling instruments for reasoning and choice making below uncertainty. As modeling languages they enable a common specification of challenge domain names with inherent uncertainty, and from a computational standpoint they help effective algorithms for computerized building and question answering. This contains trust updating, discovering the main possible reason behind the saw proof, detecting conflicts within the proof entered into the community, deciding on optimum ideas, reading for relevance, and appearing sensitivity analysis.

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

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

    • provide a well-founded useful creation to Bayesian networks, object-oriented Bayesian networks, selection bushes, impression diagrams (and editions hereof), and Markov selection processes.
    • give functional suggestion at the building of Bayesian networks, choice timber, and effect diagrams from area knowledge.
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    • give a number of examples and routines exploiting desktops for facing Bayesian networks and selection graphs.
    • present a radical advent to cutting-edge resolution and research algorithms.

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

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

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

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

Example text

16. The numbers (x, y) in the lower table represent (St = yes, St = no). Based on these two properties, what other properties can be deduced about P (U)? If the universe consists of only one variable A, then BN specifies P (A), and P (U) is uniquely determined. We shall show that this holds in general. For probability distributions over sets of variables, we have an equation called the chain rule. For Bayesian networks this equation has a special form. 1 (The general chain rule). Let U = {A1 , .

2 still holds. However, because it is unclear what it means that a likelihood statement is true, P (e) cannot be interpreted as the probability of the evidence, and P (U, e) therefore has an unclear semantics. We will not deal further with likelihood evidence. 6, probability updating in Bayesian networks can be performed using the chain rule to calculate P (U), the joint probability table of the universe. However, U need not be large before P (U) becomes intractably large. In this section, we illustrate how the calculations can be performed without having to deal with the full joint table.

In Chapter 3, we extend the modeling language, and in Part II we present other types of graphical models. As mentioned, graphical models are communication languages. They consist of a qualitative part, where features from graph theory are used, and a quantitative part consisting of potentials, which are real-valued functions over sets of nodes from the graph; in Bayesian networks the potentials are conditional probability tables. The graphical part specifies the kind of potentials and their domains.

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