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Well, I am not an expert on statistics, so maybe I'm missing something important, but I really don't understand all the negative criticism that I see in other reviews of this book. Pearl, who has spent a long career working in an area which spans statistical reasoning, philosophy and AI, set himself an extremely ambitious goal: he wanted to establish a clear, logically consistent foundation for the notions of causality ("A makes B happen") and counterfactuals ("B would have happened if A had happened"). As he says, both statisticians and philosophers had been deeply mistrustful of both concepts, preferring only to talk about associations.

Pearl gives coherent reasons to believe that that this is overcautious. Human language is packed full of causality and counterfactuals: it's the fundamental substrate of our common worldview, we can't do without it. To take just one of many flagrant examples, it's impossible to make sense of fundamental legal and moral concepts like "responsibility" or "guilt" without using this language. If the prosecutor wants to convince the court that X is guilty of murdering Y, he needs to demonstrate that Y would have been alive had it not been for X's actions. To say that this is philosophically or mathematically inadmissible is to deny the validity of the entire field of legal reasoning. If you're familiar with the philosophical tradition, your knee-jerk response at this point may be to object "but what about Hume?". Pearl looks at what Hume actually says on the subject, and points out that his revised definition of causality is not just phrased in terms of associations. He also realised that he needed to add counterfactuals.

At least on his own account, Pearl and his students appear to have made a great deal of progress in attacking these thorny problems. They have developed a way of thinking about them where the central construct is a "causal diagram", a graph where different factors are connected by arrows representing hypothesized causal links. Causal diagrams are a good match to people's intuitions about causality, and Pearl gives many examples showing how they support different kinds of reasoning. Some of this reasoning is obvious, some of it is very subtle; some of it becomes obvious only after looking at the diagrams. For example, a pattern which comes up many times in different forms is so-called "collider bias", where two causal arrows meet at the same point: if you condition on the joining concept, you'll create a spurious association. Pearl gives a cute illustration from the world of dating, where the folk wisdom is that the good-looking dates tend to be jerks. His explanation is as follows. Being good-looking and having a pleasant personality are both features that make someone more attractive. It is reasonable to suppose that these two things may not actually be correlated. But if your sample is drawn from the people you've dated, you're conditioning on the "attractiveness" variable: you're only looking at people who were attractive enough that you dated them. This creates a spurious negative association between "good-looking" and "pleasant personality". So if someone is good-looking, they are more likely to have an unpleasant personality. "Collider bias" is very simple compared to some of the things covered in the book. Particularly impressive items are the "do-calculus" (an axiomatic framework for estimating the effect of performing an intervention), and a set of formulas for measuring direct and indirect effects when one factor operates on another through an intermediary; for example, smoking causing cancer through the intermediary of tar. Pearl describes the reasoning that led him to these ideas, where in many cases a deceptively simple formula is the product of several years of careful thought.

Well, it's possible that I'm a sucker who's been taken in by good marketing. But Pearl has an excellent reputation: he's published hundreds of widely cited papers and picked up just about every award going. To me, he looks like the real deal. I think I need to read his 2009 book Causality and download a causal inference package.