Faithfulness in chain graphs: The discrete case

Authors:
Jose M. Peòa
Affiliations:
Laboratory for Intelligent Information Systems, Department of Computer and Information Science, Linköping University, SE-58183 Linköping, Sweden
Venue:
International Journal of Approximate Reasoning
Year:
2009

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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 R^d, whereas those that factorize according to G but are not faithful to it have zero Lebesgue measure wrt R^d. 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.