FUNDAMENTALS OF STATISTICAL CAUSALITY

2 Preface Traditionally, Statistics has been concerned with uncovering and describing associations, and statisticians have been wary of causal interpretations of their findings. But users of Statistics have rarely had such qualms. For otherwise what is it all for? The enterprise of " Statistical Causality " has developed to take such concerns seriously. It has led to the introduction of a variety of formal methods for framing and understanding causal questions, and specific techniques for collecting and analysing data to shed light on these. This course presents an overview of the panoply of concepts, with associated mathematical frameworks and analytic methods, that have been introduced in the course of attempts to extend statistical inference beyond its traditional focus on association, and into the realm of causal connexion. Emphasis is placed on understanding the nature of the problems addressed, on the interplay between the concepts and the mathematics, and on the relationships and differences between the various formalisms. In particular, we show how a variety of problems concerned with assessing the " effects of causes " can be fruitfully formulated and solved using statistical decision theory. Our emphasis is almost entirely on problems of " identification " , where we suppose the proba-bilistic structure of the processes generating our data is fully known, and ask whether, when and how that knowledge can be used to address the causal questions of interest. In the causal context , the more traditional statistical concern with estimation of unknown probabilistic structure from limited data is a secondary (admittedly extremely important, and currently highly active) enterprise, that will hardly be addressed here. For reasons of space and coherence, our emphasis is also largely restricted to understanding and identifying the effects of applied causes. The problem of identifying the causes of observed effects raises many further subtle issues, both philosophical and mathematical, and would take us too far afield.