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	\myheading{Module 19.7: Independencies encoded by a Bayesian network  (Case 2: Node and its non-parents)}
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				\onslide<1->{\item Now let's look at the relation between a node and its non-parent nodes.}
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				\onslide<2->{\item Is $L \perp S$?}
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				\onslide<3->{\item No, knowing the SAT score tells us about $I$ which in turn tells us something about $G$ and hence $L$}
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				\onslide<4->{\item Hence we expect $P(I^1|s^1)>P(I^1|s^0)$}
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				\onslide<5->{\item Similarly we can argue $L\not\perp D$ and $L\not\perp I$}
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				\onslide<1->{\item But what if we know the valueof $G$?}
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				\onslide<2->{\item Is $L\perp(S|G)$?}
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				\onslide<3->{\item Yes, the grade completely determines the recco letter}
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				\onslide<4->{\item Once we know the grade, other variables do not add any information}
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                \onslide<5->{\item Hence $L \perp (S|G)$}
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                \onslide<6->{\item Similarly we can argue $L\perp (I|G)$, $L\perp (D|G)$}
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                                \onslide<1->{\item But, wait a minute!}
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                                \onslide<2->{\item The instructor may also want to look at the SAT score in addition to the grade.}
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                                \onslide<3->{\item Well, we "assumed" that the instructor only relies on the grade.}
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                                \onslide<4->{\item That was our "belief" of how the world works}
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                                \onslide<5->{\item And hence we drew the network accordingly.}
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                                \onslide<1->{\item Ofcourse we are free to change our assumptions}
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                                \onslide<2->{\item We may want to assume that the instructor also looks at the SAT score}
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                                \onslide<3->{\item But if that is the case we have to change the network to reflect this dependence}
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                                \onslide<4->{\item Why just SAT score? The instructor may even consult one of his colleagues and seek his/her opinion}
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                                \onslide<1->{\item Remember: The graph is a reflection of our assumptions about how the world works}
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                                \onslide<2->{\item One assumptions about dependencies are encoded in the graph}
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                                \onslide<3->{\item Once we build the graph we freeze it and do all reasoning and analysis (independence) on this graph}
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                                \onslide<4->{\item It is not fair to ask "what if" questions involving other factors (for example, what if the professor was in a bad mood?)}
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                                \onslide<1->{\item If we believe Graph(a) is how the world works then $ L\perp (S|G)$}
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                                \onslide<2->{\item If we believe Graph(b) is how the world works then $ L\not\perp (S|G)$}
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                                \onslide<3->{\item We will stick to Graph(a) for the discussion.}
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                                \onslide<1->{\item Let's return back to our discussion of finding independence relations in the graph}
                                \onslide<2->{\item So far we have seen three cases as summarized on the next slide}
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