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Artificial Intelligence
Probabilistic reasoning in intelligent systems: networks of plausible inference
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Probabilistic inference and influence diagrams
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Axioms and algorithms for inferences involving probabilistic independence
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Causal networks: semantics and expressiveness
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d-Separation: From Theorems to Algorithms
UAI '89 Proceedings of the Fifth Annual Conference on Uncertainty in Artificial Intelligence
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The graphoid axioms for conditional independence, originally described by Dawid [1979], are fundamental to probabilistic reasoning [Pearl, 1988]. Such axioms provide a mechanism for manipulating conditional independence assertions without resorting to their numerical definition. This paper explores a representation for independence statements using multiple undirected graphs and some simple graphical transformations. The independence statements derivable in this system are equivalent to those obtainable by the graphoid axioms. Therefore, this is a purely graphical proof technique for conditional independence.