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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.

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