# For each parent of in g we know that when is not

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these variables must appear in the topological order before. For each parent of in G , , we know that when is not observed due to the active trail .Therefore,. Since all such parents must appear before in any topological order of G , all of them must be in Moreover, for each child of, that appears before in the topological order, we also know that when is not observed due to the active trail, therefore. We know that we need to consider the co-parents of Xi as well. Let’s consider a co-parent of, , that appears in the topological order before . As the name implies, is a parent of, which is a

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sibling of. In, we have the following independency , and is a parent of in . However, we are now creating an independency that is NOT in G , since observing will connect and via an active trail in G that passes though , therefore, cannot be d-separated from using the current parent set of Since each element of this parent set is necessary, we must add all such as parents of to avoid creating these extra independencies. These variables are now in fact necessary and sufficient replacement of Xi in parenting . In fact, we know that these variables are subset of the Markov Blanket of Xi , namely, they are the variables in the that appear in the topological order before. These variables shield from other variables in the network, thus using them to replace no other active trail can reach and continue to when these variables are observed. Therefore, using this set of new parents, the local Markov assumption is satisfied for in. We can explicitly create as follows :
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• Spring '13
• Dr.ZAre
• Probability theory, Pearson product-moment correlation coefficient, active trail, G. Therefore, G. Moreover, Soheila Molaei

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For each parent of in G we know that when is not observed...

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