Exercise 14.17

Consider the Bayes net shown in Figure politics-figure.

1. Which, if any, of the following are asserted by the network structure (ignoring the CPTs for now)?

1. ${\textbf{P}}(B,I,M) = {\textbf{P}}(B){\textbf{P}}(I){\textbf{P}}(M)$.

2. ${\textbf{P}}(JG) = {\textbf{P}}(JG,I)$.

3. ${\textbf{P}}(MG,B,I) = {\textbf{P}}(MG,B,I,J)$.

2. Calculate the value of $P(b,i,m,\lnot g,j)$.

3. Calculate the probability that someone goes to jail given that they broke the law, have been indicted, and face a politically motivated prosecutor.

4. A context-specific independence (see page CSI-page) 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 politics-figure?

5. Suppose we want to add the variable $P{PresidentialPardon}$ to the network; draw the new network and briefly explain any links you add.