14.14 Consider the Bayes net shown in Figure 14.23. a. Which of the following are asserted by the network structure? (i) P(B, I, M) = P(B)P(IPM). (ii) P(JG) = P(J|GI). (iii) P(MG,BI) = P(MG,B,1,J). 563 BTN PYG) 10 Figure 14.23 A simple Bayes net with Boolean variables B=Broke Election Law, I = Indicted, M = Politically Motivated Prosecutor, G = FoundGuilty, J = Jailed. b. Calculate the value of P(b, i, m.g.). c. Calculate the probability that someone goes to jail given that they broke the law, have been indicted, and face a politically motivated prosecutor. d. A context-specific independence (see page 542) allows a variable to be independent of some of its parents given certain values of others. In addition to the usual conditional independences given by the graph structure, what context-specific independences exist in the Bayes net in Figure 14.23? e. Suppose we want to add the variable P= PresidentialPardon to the network; draw the new network and briefly explain any links you add.
