Мишель за то, что они поверили моему многолетнему обещанию, что книга в конце концов будет готова. И моим внукам, Леоре, Тори, Адаму, Ари и Эвану, за то, что они придавали смысл моим долгим путешествиям и всегда разрешали мои вопросы “почему”.

Заметки

Заметки к предисловию

Students are never allowed: With possibly one exception: if we have performed a randomized controlled trial, as discussed in Chapter 4.

Заметки к главе первой

Then the opposite is true: In other words, when evaluating an intervention in a causal model, we make the minimum changes possible to enforce its immediate effect. So we “break” the model where it comes to A but not B.

We should thank the language: I should also mention here that counterfactuals allow us to talk about causality in individual cases: What would have happened to Mr. Smith, who was not vaccinated and died of smallpox, if he had been vaccinated? Such questions, the backbone of personalized medicine, cannot be answered from rung-two information.

Yet we can answer: To be more precise, in geometry, undefined terms like “point” and “line” are primitives. The primitive in causal inference is the relation of “listening to,” indicated by an arrow.

Заметки к главе второй

And now the algebraic magic: For anyone who takes the trouble to read Wright’s paper, let me warn you that he does not compute his path coefficients in grams per day. He computes them in “standard units” and then converts to grams per day at the end.

Заметки к главе пятой

“Cigarette smoking is causally related”: The evidence for women was less clear at that time, primarily because women had smoked much less than men in the early decades of the century.

Заметки к главе восьмой

And Abraham drew near: As before, I have used the King James translation but made small changes to align it more closely with the Hebrew.

The ease and familiarity of such: The 2013 Joint Statistical Meetings dedicated a whole session to the topic “Causal Inference as a Missing Data Problem”—Rubin’s traditional mantra. One provocative paper at that session was titled “What Is Not a Missing Data Problem?” This title sums up my thoughts precisely.

This difference in commitment: Readers who are seeing this distinction for the first time should not feel alone; there are well over 100,000 regression analysts in the United States who are confused by this very issue, together with most authors of statistical textbooks. Things will only change when readers of this book take those authors to task.

Unfortunately, Rubin does not consider: “Pearl’s work is clearly interesting, and many researchers find his arguments that path diagrams are a natural and convenient way to express assumptions about causal structures appealing. In our own work, perhaps influenced by the type of examples arising in social and medical sciences, we have not found this approach to aid the drawing of causal inferences” (Imbens and Rubin 2013, p. 25).

One obstacle I faced was cyclic models: These are models with arrows that form a loop. I have avoided discussing them in this book, but such models are quite important in economics, for example.

Even today modern-day economists: Between 1995 and 1998, I presented the following toy puzzle to hundreds of econometrics students and faculty across the United States:

Consider the classical supply-and-demand equations that every economics student solves in Economics 101.

1. What is the expected value of the demand Q if the price is reported to be P = p0?

2. What is the expected value of the demand Q if the price is set to P = p0?

3. Given that the current price is P = p0, what would the expected value of the demand Q be if we were to set the price at P = p1?

The reader should recognize these queries as coming from the three levels of the Ladder of Causation: predictions, actions, and counterfactuals. As I expected, respondents had no trouble answering question 1, one person (a distinguished professor) was able to solve question 2, and nobody managed to answer question 3.

The Model Penal Code expresses: This is a set of standard legal principles proposed by the American Law Institute in 1962 to bring uniformity to the various state legal codes. It does not have full legal force in any state, but according to Wikipedia, as of 2016, more than two-thirds of the states have enacted parts of the Model Penal Code.

Заметки к главе девятой

Those sailors who had eaten: The reason is that polar bear livers do contain vitamin C.

“On the Inadequacy of the Partial”: The title refers to partial correlation, a standard method of controlling for a confounder that we discussed in Chapter 7.

Here is how to define the NIE: In the original delivery room, NIE was expressed using nested subscripts, as in Y(0,M). I hope the reader will find the mixture of counterfactual subscripts and do-operators above more transparent.

In that year researchers identified: To be technically correct it should be called a “single nucleotide polymorphism,” or SNP. It is a single letter in the genetic code, while a gene is more like a word or a sentence. However, in order not to burden the reader with unfamiliar terminology, I will simply refer to it as a gene.

Библиография

Введение: ум важнее данных

Annotated Bibliography

The history of probability and statistics from antiquity to modern days is covered in depth by Hacking (1990); Stigler (1986, 1999, 2016). A less technical account is given in Salsburg (2002). Comprehensive accounts of the history of causal thought are unfortunately lacking, though interesting material can be found in Hoover (2008); Kleinberg (2015); Losee (2012); Mumford and Anjum (2014). The prohibition on causal talk can be seen in almost every standard statistical text, for example, Freedman, Pisani,