 
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
headaches'.
(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(ba) = 0.8, Pr(b¬a) =
0.2, Pr(ca) = 0.2, Pr(c¬a) = 0.05, Pr(ec) = 0.8, Pr(e¬c) = 0.6, Pr(dbc) = 0.8, Pr(db
¬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.
Answers :
(a) Sorry for an ascii drawing. The main thing here is that arcs go from cause (e.g. brain tumor)
