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Consider the graphical model in Figure 4 for a medical diagnosis example, where
= positive X-ray, and
= 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.
Graphical model for diagnosis example.
List the pairs of nodes that can be proven to be conditionally independent with the definition of d-separation, given the following evidence:
- No evidence for any of the nodes.
- The lung cancer node is set to true (and no other evidence).
- The smoker node is set to true (and no other evidence).
- The cough node is set to true (and no other evidence).