Faithfulness in chain graphs: The discrete case |
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Authors: | Jose M. Pe a |
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Affiliation: | aLaboratory for Intelligent Information Systems, Department of Computer and Information Science, Linköping University, SE-58183 Linköping, Sweden |
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Abstract: | This paper deals with chain graphs under the classic Lauritzen–Wermuth–Frydenberg interpretation. We prove that the strictly positive discrete probability distributions with the prescribed sample space that factorize according to a chain graph G with dimension d have positive Lebesgue measure wrt , whereas those that factorize according to G but are not faithful to it have zero Lebesgue measure wrt . This means that, in the measure-theoretic sense described, almost all the strictly positive discrete probability distributions with the prescribed sample space that factorize according to G are faithful to it. |
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Keywords: | Chain graphs Faithfulness Markov equivalence Factorization equivalence Largest chain graphs |
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