Understanding the flow in Graphs

In this section, let’s dig into Directed Acyclic Graphs (DAGs), which are meant to represent pathways of association and causation. The crux of this exploration is the “flow of association” within DAGs, essential for understanding node relationships, particularly their statistical dependence or independence. In this flow of association, an analysis of basic DAG structures – chains, forks, and colliders – sheds light on the (conditional) independence or dependence of node pairs, with conditional independence exemplified by the factorization of joint probabilities into conditional probabilities.

Let’s contrast simple graph structures, where disconnected nodes (see node A and node B in Figure 5.1a) indicate statistical independence, we also examine connected nodes (node B and node C in Figure 5.1a), where an edge signifies an association based on the causal edge assumption (e.g., C is associated with B). This...