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Reviewer: Ralph Walter Wilkerson

Pearl lays the mathematical foundations for an empirical investigation into causation. This book follows in the footsteps of others written by this author [1,2] that continue to expand our knowledge in trying to understand the reasoning process. The book is largely self-contained, requiring only a basic understanding of probability theory and graph theory. In fact, the first few chapters review the necessary mathematical preliminaries, as well as how to investigate data to discover cause and effect relationships. These are followed by chapters on causal effects and applications to the social sciences and economics. Simpson’s paradox and counterfactuals are discussed in later chapters alongside applications of counterfactual analysis. The book is extremely well written, and while mathematically precise, provides a thought-provoking study of causality and its implications. Online Computing Reviews Service

Reviewer: James Van Speybroeck

Pearl has taken on a difficult task, namely, using the word “causality” in statistics. Causality is anathema to the statistical researcher. Every sadistic statistics teacher waits like a hungry lion in tall grass for an undergraduate to refer to causality when first introduced to correlation analysis, and then proceeds to humiliate the novice. However, let me assure the reader that this is a serious and thorough work designed to study causality from a mathematical viewpoint, to the benefit of researchers in business and the social sciences. The first chapter wisely lays out the pinions of probability, graphs and causal models. The material is classical, but absolutely necessary for a full appreciation of the book. Chapter 2 deals with the theory of inferred causation and emphasizes Occam's Razor. Chapter 3, “Causal Diagrams and the Identification of Causal Effects,” really deals with the effect of interception. Although relatively sophisticated, the example of smoking and genotype theory in the section explaining confounding bias is well chosen. Chapter 4, “Actions, Plans, and Direct Effects,” extends the discussion of analysis of causal effects from primitive intervention to cover several new topics, such as conditional actions and stochastic policies. Chapter 5 details causality and structural models in social science and economics. The discussion of structural equation modeling is particularly well written. The citations clearly show that the author has done his homework in this area. Chapter 6, “Simpson's Paradox, Confounding, and Collapsibility,” deals with a topic—confounding— that is eliminated from many discussions of statistics. The reason for the omission concerns the very nature of confounding: to explain causality. This well-written chapter attempts to show the statistician how to formulate and manage confounding. Chapter 7 presents the concept of the “counterfactual” in a formal analysis structure. This concept is the leitmotif that runs through the remainder of the book. Through this formal analysis, many topics introduced earlier are covered in more depth, including causal models, action, causal effects, causal relevance, error terms, and exgeneity. Chapter 8 continues the sophisticated treatment of counterfactuals by using them to explore bounding effects. Chapter 9 connects probability of causation with interpretation and identification. In chapter 10, “The Actual Cause,” the author describes the impact of causality of a given outcome in a specific scenario. The epilogue of the text is a transcript of a lecture by the author. The bibliography is valuable, if not exhaustive. The author has done an excellent job of explaining a difficult topic in very understandable terms.