Problem 2 A description of how to enter so-called likelihood evidence in both Netica and Hugin software is given in Figure 3.15. In ????3.4 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 X-ray 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

????X-ray
 

???? 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.