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Probabilistic relevance relations

The intuition behind the construction of Bayesian networks and other graph-based representations of joint probability distributions from expert judgments is based on the assumed relationship between "connectedness" in the graphical model and "relatedness" among the variables involved. We show that several plausible definitions of relatedness do not adhere to such an equivalence. We then provide a definition of probabilistic relatedness that is closely related to connectedness in the graphical model and prove that the two concepts are equivalent whenever the model uses only propositional variables and assuming every combination of value assignment to these variables is feasible. We conjecture that the equivalence established holds also when these restrictions are lifted.