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d-separation [4* P]

Figure: Graphical model for diagnosis example.
\includegraphics[width=7cm]{./fig_dseparation.eps}

Consider the graphical model in Figure 1 for a medical diagnosis example, where $ B$ = bronchitis, $ S$ = smoker, $ C$ = cough, $ X$ = positive X-ray, and $ L$ = lung cancer. Suppose that the prior for a patient being a smoker is 0.25, and the prior for the patient having bronchitis is 0.05.

List the pairs of nodes that can be proven to be conditionally independent with the definition of d-separation, given the following evidence:

a)
[1* P] No evidence for any of the nodes.
b)
[1* P] The lung cancer node is set to true (and no other evidence).
c)
[1* P] The smoker node is set to true (and no other evidence).
d)
[1* P] The cough node is set to true (and no other evidence).



Haeusler Stefan 2007-12-03