.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 p and l 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 p and l 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?

Problem 2 A description of how to enter so-called likelihood evidence in Netica, BayesiaLab and Hugin software is given in Figure 3.19. In x3.4 we only looked at an example where we added virtual evidence for a root node; however it can be added for any node in the network. Consider the cancer example from Chapter 2 (supplied as Netica file cancer.dne). Suppose that the radiologist who has taken and analyzed the Xray in this cancer example is uncertain. He thinks that the X-ray looks positive, but is only 80% sure.
Add this evidence as a likelihood ratio of 4:1.
Work out the likelihood ratio that needs to be used to produce a new belief of Bel(X-ray) = 0:8 Add this likelihood ratio as evidence to confirm your calculations.
Add an explicit virtual node V to represent the uncertainty in the observation.
Confirm that adding specific evidence for V gives the same results as adding the likelihood evidence.

S X C B