Faithfulness in Chain Graphs: The Gaussian Case
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This paper deals with chain graphs under the classic Lauritzen-Wermuth-Frydenberg interpretation. We prove that the regular Gaussian distributions that factorize with respect to a chain graph G with d parameters have positive Lebesgue measure with respect to R^d, whereas those that factorize with respect to G but are not faithful to it have zero Lebesgue measure with respect to R^d. This means that, in the measure-theoretic sense described, almost all the regular Gaussian distributions that factorize with respect to G are faithful to it.
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