Consider the Bayes net shown in Figure politics-figure
.
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Which of the following are asserted by the network structure?
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${\textbf{P}}(B,I,M) = {\textbf{P}}(B){\textbf{P}}(I){\textbf{P}}(M)$ . -
${\textbf{P}}(J|G) = {\textbf{P}}(J|G,I)$ . -
${\textbf{P}}(M|G,B,I) = {\textbf{P}}(M|G,B,I,J)$ .
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Calculate the value of
$P(b,i,\lnot m,g,j)$ . -
Calculate the probability that someone goes to jail given that they broke the law, have been indicted, and face a politically motivated prosecutor.
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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?
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Suppose we want to add the variable
$P={PresidentialPardon}$ to the network; draw the new network and briefly explain any links you add.