A Rooster Crow Does Not Cause the Sun To Rise
Ranajit Chakraborty · Human Biology · 2001
This book is about the formal analyses of cause-effect relationships between sets of observed events and/or underlying variables related to them. Through ten chapters and an exquisitely well-written epilogue, the author, a prolific computer science specialist, essentially "demystifies" the concept of causality and explains its mathematical, statistical, as well as philosophical implications. Along with brief background material on probability theory and graph theory, the first chapter presents the basic paradigms and major problems of causal analysis and sets the tone for what follows in the subsequent chapters. The most difficult question, what constitutes evidence of a cause-effect relationship in observed data, is discussed in chapter 2, ending with the conceptualization of the validity of any such relationship observed. Chapters 3 and 4 get into deeper theoretical treatments of prediction of direct and indirect effects of actions and policies based on data in the presence of an incomplete understanding of the existence of a cause-effect relationship. Identifiability of cause-effect relationship is the central theme of these chapters. The implications of the calculus of intervention, thus developed, are discussed in the context of applications to social and health science problems in chapter 5 and 6, where the popular constructs of structural equations and confounding are presented. In contrast to the graph theory treatment of detecting the presence of confounding and of identifying critical variables that control the effect of confounding (discussed in chapter 3), chapter 6 presents the difficulties of defining and controlling confounding when statistical criteria are used. The theories of counterfactuals and structural models are presented in chapter 7, through which more rigorous definitions of the concepts introduced earlier in the book are obtained. These include concepts such as causal models, action, causal effects, causal relevance, error terms, and exogeneity. The last three chapters (8 through 10) constitute applications of counterfactual analysis. They include methods of the developing bounds of causal relationship from data of imperfect experiments using combinations of graphical and counterfactual models (chapter 8), identification and interpretation of probability of causation (chapter 9), and a formal explication of the notion of "actual cause" (chapter 10).