Let B = (G,P) be a Bayesian network over some set of variables X. Consider some subset of evidence nodes Z, and let X be all of the ancestors of the nodes in Z. Let B' be a network over the induced subgraph over X, where the CPD for every node x in X is the same in B' as in B. Prove that the joint distribution over X is the same in B as in B'. The nodes in X' - X are called barren nodes relative to X, because
(when not instantiated) they are irrelevant to computations concerning X