By Finn V. Jensen (auth.)

ISBN-10: 1475735022

ISBN-13: 9781475735024

ISBN-10: 1475735049

ISBN-13: 9781475735048

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

**Example text**

To each variable A with parents BI, ... , B n , there is attached the potential table P(A I B I ,···, Bn). Note that if A has no parents, then the table reduces to unconditional probabilities P(A). 14, the prior probabilities P(A) and P(B) must be specified. It has been claimed that prior probabilities are an unwanted introduction of bias to the model, and calculi have been invented in order to avoid it. 9). The definition of Bayesian networks does not refer to causality, and there is no requirement that the links represent causal impact.

Show that A is d-separated from the remaining uninstantiated variables. 5 Let Dl and D2 be DAGs over the same variables. Dl is an I-submap of D2 if all d-separation properties of Dl also hold for D 2. If also D2 is an I-submap of Db they are said to be I-equivalent. 19 are I-equivalent? 19. 5. 14). 15, a joint probability table for the binary variables A, B, and C is given. 32 1. 14. 6. 15. 7. (i) Calculate P(B, C) and P(B). (ii) Are A and C independent given B? 5. (i) Show that P(B I A, C) = P(B I A).

Having identified the variables for the model, the next thing will be to establish the directed links for a causal network. 1 Milk test Milk from a cow may be infected. To detect whether the milk is infected, you have a test, which may give either a positive or a negative test result. The test is not perfect. It may give a positive result on clean milk as well as a negative result on infected milk. We have two hypothesis events: milk infected and milk not infected, and because they are mutually exclusive, they are grouped into the variable Infected?

### Bayesian Networks and Decision Graphs by Finn V. Jensen (auth.)

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