Hint consider all active trails x 1 x 2 x n that go

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((Hint : Consider all active trails, X 1 X 2 · · · X n that go through Alarm, make sure that there still an active trail under the same conditions – i.e. observed variables– between X 1 and X n in the marginalized network.) 3
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Figure 3: Burglar Alarm Network 2. Generalize the procedure you used to solve the above into a node-elimination algorithm. That is, define an algorithm that transforms the structure of G into G such that one of the nodes X l of G is not in G and G is an I–map of the marginal distribution over the remaining variables as defined by G . (Hint: Consider the relationship between the variables you added edges to in part 1 and the node being marginalized. Now, can you devise a set of generic rules over these affected variables? It would be helpful to think about different local configurations around X l ) 4
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