Probabilistic Methods for Bioinformatics

Chapter 6 Further Properties of Bayesian Networks

The previous chapter introduced only one relationship between probability distributions and DAGs, namely the Markov condition. However, the Markov condition entails only independencies; it does not entail any dependencies. That is, when we only know that (G, P) satisfies the Markov condition, we know that the absence of an edge between X and Y entails there is no direct dependency between X and Y, but the presence of an edge between X and Y does not mean there is a direct dependency. In general, we would want an edge to mean there is a direct dependency. In Section 6.2, we discuss another condition, ...