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