By Uffe B. Kjærulff, Anders L. Madsen

*Bayesian Networks and effect Diagrams: A consultant to building and research, moment Edition,* provides a accomplished advisor for practitioners who desire to comprehend, build, and research clever platforms for determination help in accordance with probabilistic networks. This new version comprises six new sections, as well as fully-updated examples, tables, figures, and a revised appendix. meant essentially for practitioners, this booklet doesn't require refined mathematical talents or deep realizing of the underlying concept and techniques nor does it talk about substitute applied sciences for reasoning lower than uncertainty. the speculation and strategies offered are illustrated via greater than a hundred and forty examples, and workouts are integrated for the reader to examine his or her point of realizing. The ideas and strategies offered for wisdom elicitation, version building and verification, modeling options and tips, studying versions from information, and analyses of versions have all been built and sophisticated at the foundation of diverse classes that the authors have held for practitioners around the globe.

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**Additional resources for Bayesian Networks and Influence Diagrams: A Guide to Construction and Analysis**

**Sample text**

In Chapter 3 we shall see that if a joint probability distribution factorizes according to the structure of a DAG, then the DAG is a graphical representation of the independence properties of the distribution. , the directed links should point from cause to eﬀect). Otherwise, problems might arise both in terms of getting the right (conditional) independence properties of the network and in terms of ease of speciﬁcation of the conditional probabilities (parameters) of the network. This important issue will be further discussed in Chapter 4 and Chapter 6.

3 using the directed global Markov criterion. 3 Probabilities As mentioned in Chapter 2, probabilistic networks have a qualitative aspect and a corresponding quantitative aspect, where the qualitative aspect is given by a graphical structure in the form of an acyclic, directed graph (DAG) that represents the (conditional) dependence and independence properties of a joint probability distribution deﬁned over a set of variables that are indexed by the vertices of the DAG. The fact that the structure of a probabilistic network can be characterized as a DAG derives from basic axioms of probability calculus leading to recursive factorization of a joint probability distribution into a product of lower-dimensional conditional probability distributions.

N − 1; vi is then an ancestor of vj and vj a descendant of vi for each j > i. The set of ancestors and descendants of v are denoted an(v) and de(v), respectively. 2 for the naming conventions used for vertices and variables. 20 2 Networks called the non-descendants of v. The ancestral set An(U) ⊆ V of a set U ⊆ V of a graph G = (V, E) is the set of vertices U ∪ u∈U an(u). A path v1 , . . , vn from v1 to vn of an undirected graph, G = (V, E), is blocked by a set S ⊆ V if {v2 , . . , vn−1 } ∩ S = ∅.