Problem 1 Consider (again — see Problem 2.8, Chapter 2) the belief network for another version of the medical diagnosis example, where B=Bronchitis, S=Smoker, C=Cough, X=Positive X-ray and L=Lung cancer and all nodes are Booleans. Suppose that the prior for a patient being a smoker is 0.25, and the prior for the patient having bronchitis

(during winter in Melbourne!) is 0.05.

Suppose that evidence is obtained that a patient has a positive X-ray result and a polytree message passing algorithm was to be used to perform belief updating.
1. Write down the ???? and values for the following nodes: S, B, C, X.
2. Show the 3 stages of data propagation by the message passing algorithm in terms of the ???? and messages.
3. Suppose that a doctor considered that smoking was a contributing factor towards getting bronchitis as well as cancer. The new network structure reflecting this model is as follows.

Why is the polytree message passing algorithm unsuitable for performing belief updating on this network?

Transcribed Image Text:

L S X C B