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And the set d-separations the dag subset ind

10.1. ALGORITHMS ASSUMING FAITHFULNESS

559
X W X
Y Z Y
(a) (b)

Example 10.13 Suppose V = {X, Y, Z, W} and

IND = {I({X}, {Z}|{Y, W}), I({Y }, {W}|{X, Z})}.

560 X
H1

H2

Y

Z

W
X Y Z W

Figure 10.15: Given V = {X, Y, Z, W, T} and IND consists of the d-separations in the DAG in (a) restricted to these variables, Algorithm 10.4 will produce the DAG in (b) or one with W → T instead of W ← T.

pattern containing the d-separations. The next example shows a situation in which the output of Algorithm 10.4 is a DAG, but the set of d-separations in the DAG is not a subset of IND.

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and the set dseparations the dag subset ind
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