From Bayesian Networks to Causal Networks

This paper demonstrates the use of graphs as a mathematical tool for expressing independencies, and as a formal language for communicating and processing causal information for decision analysis. We show how complex information about external interventions can be organized and represented graphically and, conversely, how the graphical representation can be used to facilitate quantitative predictions of the effects of interventions. We first review the theory of Bayesian networks and show that directed acyclic graphs (DAGs) offer an economical scheme for representing conditional independence assumptions and for deducing and displaying all the logical consequences of such assumptions. We then introduce the manipulative account of causation and show that any DAG defines a simple transformation which tells us how the probability distribution will change as a result of external interventions in the system. Using this transformation it is possible to quantify, from non-experimental data, the effects of external interventions and to specify conditions under which randomized experiments are not necessary. As an example, we show how the effect of smoking on lung cancer can be quantified from non-experimental data, using a minimal set of qualitative assumptions. Finally, the paper offers a graphical interpretation for Rubin’s model of causal effects, and demonstrates its equivalence to the manipulative account of causation. We exemplify the tradeoffs between the two approaches by deriving nonparametric bounds on treatment effects under conditions of imperfect compliance.