Causal Inference in Statistics: A Primer Judea Pearl, Madelyn Glymour and Nicholas P. Jewell John Wiley & Sons, 2019, 156 pages, $46.75, paperback ISBN: 978‐1‐1191‐8684‐7

Readership: Graduate students and researchers interested in causal inference.

This book, initially originating from course notes, covers the basics of causal inference in statistics. Often classical statistical methods fail to uncover the intrinsic mechanisms that lead to the data, staying on the side of shallow somewhat descriptive interpretations. Especially in observational studies, the design of the experiment and the statistical model built to make inferences from it do not match the set of mechanistic questions the researcher would like to answer. When this is the case, the researcher can often formulate a different (ideal) design of the experiment and a different mechanistic model supporting it that would be capable of answering the mechanistic questions. Rather than declare the current experiment useless, we may ask ‘Is it possible to make inferences from the current data that would relate to the meaningful parameters of the mechanistic model?’. Over the last two decades we have seen an explosion of interest in such questions handled by the causal inference methodology. The book is meant to be an introduction to this theory. The field is very young, so even a primer book needs to refer to fairly recent literature to explain the concepts and the methods of causal inference. An introductory book in this field is a challenge as many concepts are debated, and the classic historical core of the theory may still be fluid. However, the book admirably navigates this challenge and does help a novice in the field understand its principles and concepts. This is made possible by keeping the mathematical methods confined to basic probability and by always motivating and illustrating the methods by real‐life examples. I especially enjoyed a collision of the immediate intuition of a novice trying to make sense of an example with the real picture that starts to emerge as the example is peeled deeper using causal concepts.

The book starts with Chapter 1 that motivates the rest of the book by introducing the Simpson's paradox illustrating the phenomenon of confounding brought to the extreme. It is followed by a description of the basic probability and statistics tools that are used in the rest of the book. An introduction to statistical dependence follows with reference to their applications in the context of different models. Basic model structures are expressed through equations as well as through graphs. The book explains how these representations are linked and how they can be recognised based on the data at hand.

Chapter 2 presents very useful graphical tools that summarise the key ingredients and structure of the causal models. Well‐defined graphical elements such as forks, chains, colliders, and the idea of d‐separation allow us to dissect the structure of a causal model relevant to dependencies without having to provide a full probabilistic quantitative specification of the model.

Chapter 3 brings these tools to use to ascertain the causal effects of interventions. A concept of graph surgery is introduced to transform the current model for the data into a model of the ideal experiment that allows for clear unconfounded assessment of the causal effect of the intervention. Adjustments are worked out that allow us to use the statistics based on the current model to predict the relevant quantities (structural parameters) in the causal model. A detailed application for linear models is presented.

Chapter 4 introduces a general approach of counterfactuals. In some sense, this approach generalises the methods presented in the book earlier. This chapter is somewhat more advanced conceptually, and some of the facts are presented without proof.

While maintaining mathematical rigour, the book skillfully avoids complex mathematics. This makes it suitable for statisticians who are looking to start using causal modelling in their work or to epidemiologists who are comfortable with basic probability and statistics tools. However, this does not mean that the book is easy reading. The flow of new concepts is pretty dense and concise for somebody na've to causal inference. However, overall, the book is an outstanding introduction to an exciting and very useful subject.

统计中的因果推断：《朱迪亚·珀尔（Judea Pearl），玛德琳·格利默（Madelyn Glymour）和尼古拉斯·P·珠宝（Nicholas P.Jewell John Wiley＆Sons）》，2019年，156页，46.75美元，平装本ISBN：978-1-11191-18684-7

读者群：对因果推理感兴趣的研究生和研究人员。

这本书最初源于课程笔记，涵盖了统计学中因果推理的基础。通常，经典的统计方法无法揭示导致数据产生的内在机制，而停留在浅层的描述性解释方面。特别是在观察性研究中，实验的设计和用来从中进行推断的统计模型与研究人员想要回答的一系列机械问题不匹配。在这种情况下，研究人员通常可以制定不同的（理想的）实验设计和支持该问题的不同的机械模型，从而能够回答机械问题。与其宣布当前实验没有用，我们可能会问：“是否有可能从当前数据中得出与机械模型有意义的参数有关的推论？”。在过去的二十年中，我们发现因果推理方法处理的此类问题引起了人们的极大兴趣。这本书是对这种理论的介绍。这个领域还很年轻，因此即使是入门书也需要参考相当近期的文献来解释因果推理的概念和方法。该领域的入门书是一个挑战，因为许多概念都在辩论中，并且该理论的经典历史核心可能仍然是不确定的。然而，这本书令人钦佩地克服了这一挑战，并确实帮助该领域的新手了解了其原理和概念。通过将数学方法限制在基本概率范围内，并始终通过现实生活中的实例来激发和说明这些方法，可以实现这一点。我特别喜欢新手的直觉，试图用一个真实的画面来理解一个例子，而这个真实的画面随着因果关系的概念被更深入地理解而开始显现出来。

该书从第1章开始，通过介绍辛普森悖论来激发本书的其余部分，该悖论阐明了混杂现象的极端性。其后是本书其余部分中使用的基本概率和统计工具的说明。统计依赖性的介绍将参考它们在不同模型中的应用。基本模型结构通过方程式和图形表示。本书解释了这些表示形式是如何链接的以及如何根据现有数据进行识别。

第2章介绍了非常有用的图形工具，总结了因果模型的关键成分和结构。清晰定义的图形元素（例如叉子，链条，对撞机和d分离的概念）使我们可以剖析与依存关系相关的因果模型的结构，而不必提供模型的完整概率定量说明。

第3章将使用这些工具来确定干预措施的因果关系。引入了图形手术的概念，以将数据的当前模型转换为理想实验的模型，该模型允许对干预的因果关系进行清晰无误的评估。进行了调整，使我们能够使用基于当前模型的统计信息来预测因果模型中的相关量（结构参数）。提出了线性模型的详细应用。

第4章介绍了反事实的一般方法。从某种意义上说，这种方法概括了本书前面介绍的方法。本章在概念上有些高级，有些事实没有证据。

在保持数学严格性的同时，本书巧妙地避免了复杂的数学。这使得它适合希望在工作中使用因果模型的统计学家，或者适合于基本概率和统计学工具的流行病学家。但是，这并不意味着这本书易于阅读。对于那些因果推理的人来说，新概念的流动非常密集和简洁。但是，总的来说，这本书是对令人兴奋且非常有用的主题的出色介绍。