Advanced Properties of Bayesian Networks
Richard E. Neapolitan, Xia Jiang · 2018
A Bayesian network can have a large number of nodes, and the conditional probability of a given node can be affected by instantiating a distant node. This chapter discusses intuitively how dependencies can be transmitted and blocked in a DAG. Recall that a DAG entails a conditional independency if every probability distribution, which satisfies the Markov condition with the DAG, must have the conditional independency, and Theorem 8.1 states that all and only d-separations are entailed conditional independencies. The chapter shows precisely what conditional independencies are entailed by the Markov condition. It shows two examples of probability distributions that satisfy the Markov condition with a DAG and contain a conditional independency that is not entailed by the DAG. The chapter represents a Markov equivalence class with a graph that has the same links and the same uncoupled head-to-head meeting as the DAGs in the class.