G53KRR exercise on Bayesian networks. This is exercise 2 after Chapter 12 in Brachman and Levesque's book 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(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. Answers : (a) Sorry for an ascii drawing. The main thing here is that arcs go from cause (e.g. brain tumor) Collections: Computer Technologies and Information Sciences