Graphical Models , Causality

I am grateful for the opportunity to respond to these two excellent papers. Although graphical models are intuitively compelling for conceptualizing statistical associations, the scientiic community generally views such models with hesitancy and suspicion. The two papers before us demonstrate the use of graphs { speciically, directed acyclic graphs (DAGs) { as a mathematical tool of great versatility and thus promise to make graphical languages more common in statistical analysis. In fact, I nd my own views in such close agreement with those of the authors that any attempt on my part to comment directly on their work would amount to sheer repetition. Instead, as the editor suggested, I would like to provide a personal perspective on current and future developments in the areas of graphical and causal modeling. 1 I will focus on the connection between graphical models and the notion of causality in statistical analysis. This connection has been treated very cautiously in the papers before us 2 and I would like to supplement the discussion with an account of how causal models and graphical models are related. It is generally accepted that, because they provide information about the dynamics of the system under study, causal models, regardless of how they are discovered or tested, are more useful than associational models. In other words, whereas the joint distribution tells us how probable events are and how probabilities would change with subsequent observations, 1 A complementary account of the evolution of belief networks is given in 4]. 2 In 3], the graphs were called \causal networks," for which the authors were criticised; they have agreed to refrain from using the word \causal." In the current paper, Spiegelhalter etal. deemphasize the causal interpretation of the arcs in favor of the \irrelevance" interpretation (page 4). I think this retreat is regrettable for two reasons: rst, causal associations are the primary source of judgments about irrelevance and, second, rejecting the causal interpretation of arcs prevents us from using graphical models for making legitimate predictions about the eeect of actions. Such predictions are indispensable in applications such as treatment management and patient monitoring.