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Conditional Independence [2+2* P]

Consider the graphical model in Figure 4 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.

Figure 4: Graphical model for diagnosis example.
\includegraphics[scale = 0.8]{belief_network.eps}

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

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



Pfeiffer Michael 2006-01-18