Summary: G53KRR exercise on Bayesian networks.
This is exercise 2 after Chapter 12 in Brachman and Levesque's book:
Consider the following example: Metastatic cancer is a possible cause of a brain tumor and is
also an explanation for an increased total serum calcium. In turn, either of these could cause a
patient to fall into occasional coma. Severe headache could also be explained by a brain tumor.
(a) Represent these causal links in a belief network. Let a stand for `metastatic cancer', b for
`increased total serum calcium', c for `brain tumor', d for `occasional coma', and e for `severe
(b) Give an example of an independence assumption that is implicit in this network.
(c) Suppose the following probabilities are given: Pr(a) = 0.2, Pr(b|a) = 0.8, Pr(b|¬a) =
0.2, Pr(c|a) = 0.2, Pr(c|¬a) = 0.05, Pr(e|c) = 0.8, Pr(e|¬c) = 0.6, Pr(d|bc) = 0.8, Pr(d|b
¬c) = 0.8, Pr(d|¬b c) = 0.8, Pr(d|¬b ¬c) = 0.05 and assume that it is also given that
some patient is suffering from severe headaches but has not fallen into a coma. Calculate
joint probabilities for the eight remaining possibilities (that is, according to whether a, b,
and c are true or false).
(d) According to the numbers given, the a priori probability that the patient has metastatic
cancer is 0.2. Given that the patient is suffering from severe headaches but has not fallen
into a coma, are we now more or less inclined to believe that the patient has cancer? Explain.
(a) Sorry for an ascii drawing. The main thing here is that arcs go from cause (e.g. brain tumor)