By Thomas Dyhre Nielsen, FINN VERNER JENSEN

Probabilistic graphical types and selection graphs are robust modeling instruments for reasoning and selection making less than uncertainty. As modeling languages they permit a average specification of challenge domain names with inherent uncertainty, and from a computational point of view they help effective algorithms for automated development 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, settling on optimum options, interpreting 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 kinds of frameworks via examples and workouts, which additionally teach the reader on find out how to construct those versions.

The e-book is a brand new variation of *Bayesian Networks and choice Graphs* by way of Finn V. Jensen. the recent version is dependent into elements. the 1st half specializes in probabilistic graphical types. in comparison with the former booklet, the recent version additionally encompasses a thorough description of modern extensions to the Bayesian community modeling language, advances in distinct 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 past variation, it additionally introduces Markov determination strategies and partly ordered determination difficulties. The authors additionally

- provide a well-founded useful advent to Bayesian networks, object-oriented Bayesian networks, determination bushes, impact diagrams (and variations hereof), and Markov selection processes.
- give useful suggestion at the development of Bayesian networks, determination bushes, and effect diagrams from area knowledge.
- give numerous examples and workouts exploiting computers for facing Bayesian networks and determination graphs.
- present an intensive creation to cutting-edge answer and research algorithms.

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

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**Additional resources for Bayesian Networks and Decision Graphs**

**Sample text**

2. Consider the experiment of rolling a red and a blue fair sixsided die. Give an example of a sample space for the experiment along with probabilities for each outcome. Suppose then that we are interested only in the sum of the dice (that is, the experiment consists in rolling the dice and adding up the numbers). Give another example of a sample space for this experiment and probabilities for the outcomes. 3. Consider the experiment of ﬂipping a fair coin, and if it lands heads, rolling a fair four-sided die, and if it lands tails, rolling a fair six-sided die.

10. 11. Let {A1 , . . , An } be a topological ordering of the variables in a Bayesian network, and consider variable Ai with parents pa(Ai ). Prove that Ai is d-separated from {A1 , . . , Ai−1 } \ pa(Ai ) given pa(Ai ). 12. 20. Which conditional probability tables must be speciﬁed to turn the graph into a Bayesian network? 13. 22 the structure of a simple Bayesian network is shown. 1. Are A and C d-separated given B? Are A and C conditionally independent given B? B A C Fig. 22. 13. 5. P (B | A).

Using P (R) and P (B), what is the probability distribution for your sample space? 9. 15. Recast the sample space as variables. What is the probability distribution for each variable? 10. Prove the fundamental rule for variables: P (A, B) = P (A | B)P (B) . 11. 16). 16. 11. 12. 17 describes a test T for an event A. 001 is the frequency of false positives. (i) The police can order a blood test on drivers under the suspicion of having consumed too much alcohol. The test has the above characteristics.