Faithfulness in chain graphs: The discrete case
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. (C) 2009 Elsevier Inc. All rights reserved.
faithfulness chain graphs markov equivalence factorization equivalence largest chain graphs