Causality: Models, Reasoning, and Inference (original) (raw)

2005, Journal of the American Statistical Association

Judea Pearl has been at the forefront of research in the burgeoning field of causal modeling, and Causality is the culmination of his work over the last dozen or so years. For philosophers of science with a serious interest in causal modeling, Causality is simply mandatory reading. Chapter 2, in particular, addresses many of the issues familiar from works such as Causation, Prediction and Search by Peter Spirtes, Clark Glymour, and Richard Scheines (New York: Springer-Verlag, 1993). But philosophers with a more general interest in causation will also profit from reading Pearl's book, especially the material in chapters 7, 9, and 10 (not to mention the delightful epilogue), which is selfcontained and less technical than other parts of the book. The present review is aimed primarily at readers of the second type. Pearl represents a system of causal relationships by a causal model. A causal model consists of a set of variables, a set of functions, and a probability measure representing our ignorance of the actual values of the variables. Each function generates an equation of the form V i = f i (V i1 ,…,V im), where V i is distinct from each V ij. These equations represent "mechanisms" whereby the value of one variable is causally determined by the values of others. Mechanisms differ from what philosophers call "laws" in that the former are asymmetric. If it is a law that Y = f(X) (and f is an invertible function), then it is also a law that X = f-1 (Y). By contrast, if a causal model contains the mechanism Y = f(X), then it will not also contain the mechanism X = f-1 (Y) (except in very special cases). The system of equations may be represented qualitatively in a directed graph, with an "arrow" drawn from V i to V j just in case V i figures in the function for V j. The directed graph representation greatly facilitates inferences about the model. A causal model may be used to evaluate counterfactuals of the following form: if the value of V i were v i , then the value of V j would be …. The resultant value of V j is determined by replacing the equation V i = f i (V i1 ,…,V im) with V i = v i , and then solving the resulting system of equations. This replacement indicates that V i is set directly to v i by an intervention from outside the system, rather than having its value causally determined by the values of the variables within the system. The intervention need not be miraculous: mechanisms are not inviolable laws, but rather ceteris paribus laws that can be disrupted by external interventions. Such an intervention will not affect the functional forms of the other mechanisms in the causal system: the mechanisms are autonomous. The bulk of Pearl's book deals with inference problems where we have only partial information about the causal system being modeled. Our partial information may be of various kinds. Observational evidence may give us information about probabilistic correlations between variables; background assumptions may give us information about the graphical structure; and con