Faithfulness in Chain Graphs: The Gaussian Case

Details Faithfulness in Chain Graphs: The Gaussian Case Faithfulness in Chain Graphs: The Gaussian Case

2010-08-13

arxiv.org/abs/1008.2277v1

Statistics

Machine Learning

Scientific paper

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 $\mathbb{R}^d$, whereas those that factorize with respect to $G$ but are not faithful to it have zero Lebesgue measure with respect to $\mathbb{R}^d$. 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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