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# d-separation II [3 P]

Let be a random variable corresponding to some node in a Bayesian Network. Denote by the set of all variables in the system (i.e. variables that correspond to some node in the Network) except for .

Find the smallest set of nodes so that , i.e. variable is conditionally independent of all other variables in given . Use the fact that is conditionally independent of all its non-descendants given its parents (this is true by construction of the Bayesian Network). Specify precisely what types of nodes (their relation to ) have to be included in and explain why.

Haeusler Stefan 2010-01-26