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Causal Inference in Statistics: A Primer
CAUSAL INFERENCE IN STATISTICSA PrimerCausality is central to the understanding and use of data. Without an understanding of cause-effect relationships, we cannot use data to answer questions as basic as "Does this treatment harm or help patients?" But though hundreds of introductory texts are available on statistical methods of data analysis, until now, no beginner-level book has been written about the exploding arsenal of methods that can tease causal information from data.Causal Inference in Statistics fills that gap. Using simple examples and plain language, the book lays out how to define causal parameters; the assumptions necessary to estimate causal parameters in a variety of situations; how to express those assumptions mathematically; whether those assumptions have testable implications; how to predict the effects of interventions; and how to reason counterfactually. These are the foundational tools that any student of statistics needs to acquire in order to use statistical methods to answer causal questions of interest.This book is accessible to anyone with an interest in interpreting data, from undergraduates, professors, researchers, or to the interested layperson. Examples are drawn from a wide variety of fields, including medicine, public policy, and law; a brief introduction to probability and statistics is provided for the uninitiated; and each chapter comes with study questions to reinforce the readers understanding.
160 pages, Kindle Edition
First published March 14, 2016
About the author
Judea Pearl
32 books227 followersJudea Pearl is an Israeli-American computer scientist and philosopher, best known for championing the probabilistic approach to artificial intelligence and the development of Bayesian networks.
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Displaying 1 - 25 of 25 reviews
September 8, 2019
I read this book because I was so impressed with the importance of causal inferencing from data, as Pearl has developed it, in his more popular book, "The Book of Why". But that book didn't present enough detail for me to actually apply causal analysis to my own data. I hoped that a self-styled "Primer" would fill that gap.
Unfortunately, this book did not help.
The material is presented in a highly abstract way. The examples are unecessarily complicated by mathematical abstraction. For example, if you want to know whether sexual discrimination causes a hiring decision, one of his examples, you would call the effect "hiring" and one of the causes "the sex of the candidate". But Pearl calls them Y and X. Surely H and S would make it easier to follow, if one is too terse to use "Hiring" and "Sex". Every example is recast into this abstract-ese. In fact, every cause is "X" and every effect "Y". This makes the examples confusing for people who learn from example. A Primer, in my opinion, should guide the reader with examples.
Also, a Primer, I think, should have worked examples. The reader should be given case studies to work through. But there should also be some explanation of how to perform those case studies, so that one can check whether they understand the material. This book has plenty of case studies. But they are typically either very abstract, or rely on X's and Y's rather than the actual content of the example. And there are no solutions.
The book also seems to be organized chronologically by what Pearl has figured out, rather than by the subject matter. It seems like each chapter says this "we want to do this thing, the stuff I showed in the last chapter wasn't good enough, but in this chapter I'll show you something better." By the time one gets to chapter 4 (the last one), one seems to be able to conclude that everything else is a special case of counterfactual reasoning, and many (most?) of the tools are subsumed by a new set of tools you only learn about as the book is ending.
Also, there are many typos, some even in the equations, which change the meaning of the text.
I left the book without the ability to do the kind of analysis I need to do. A real Primer, rather than a re-telling of material from his larger statistical tome, would have been really, really nice.
Unfortunately, this book did not help.
The material is presented in a highly abstract way. The examples are unecessarily complicated by mathematical abstraction. For example, if you want to know whether sexual discrimination causes a hiring decision, one of his examples, you would call the effect "hiring" and one of the causes "the sex of the candidate". But Pearl calls them Y and X. Surely H and S would make it easier to follow, if one is too terse to use "Hiring" and "Sex". Every example is recast into this abstract-ese. In fact, every cause is "X" and every effect "Y". This makes the examples confusing for people who learn from example. A Primer, in my opinion, should guide the reader with examples.
Also, a Primer, I think, should have worked examples. The reader should be given case studies to work through. But there should also be some explanation of how to perform those case studies, so that one can check whether they understand the material. This book has plenty of case studies. But they are typically either very abstract, or rely on X's and Y's rather than the actual content of the example. And there are no solutions.
The book also seems to be organized chronologically by what Pearl has figured out, rather than by the subject matter. It seems like each chapter says this "we want to do this thing, the stuff I showed in the last chapter wasn't good enough, but in this chapter I'll show you something better." By the time one gets to chapter 4 (the last one), one seems to be able to conclude that everything else is a special case of counterfactual reasoning, and many (most?) of the tools are subsumed by a new set of tools you only learn about as the book is ending.
Also, there are many typos, some even in the equations, which change the meaning of the text.
I left the book without the ability to do the kind of analysis I need to do. A real Primer, rather than a re-telling of material from his larger statistical tome, would have been really, really nice.
May 8, 2021
This book was much more understandable than Pearl's textbook Causality, which we tried to read in my technical book club, but hit a wall pretty quickly. Causality suffered from many issues, most notably confusing notation and terminology (as one very small example, using "path" to mean "undirected path" in a directed graph). This is pretty common in math books, but it's usually possible to disambiguate the meaning of terms by reading the proofs. Pearl didn't include proofs in that book, which meant that reading it was like backtracking through a set of possible meanings for variables and terms. In short, if you're interested in learning the contents of this book but aren't already pretty expert on these topics, you almost certainly want to at least start with this book instead of the other, more famous Judea Pearl book on the topic.
While this book didn't include proofs either, it does include practical and fully worked examples, along with exercises (and a partial solutions manual available online). It's also much shorter, which is a big benefit.
For reading this book for self-study, I'd recommend the following:
1. There are many errors in the book, and it's worth marking up your copy with the errata. Some of the errors are things like critical missing terms in a few key equations or typos in exercises that make them difficult to do.
2. When doing the exercises, many of them can be checked by writing out structural equations and generating a faked data set (e.g. with numpy) by sampling from a distribution that matches the parameters of the problem. Then you know the "right" answer (e.g. how big a particular coefficient is), and you can make sure that your interpretation of the techniques generate an answer that matches it. My reading partner and I found many errors in our solutions this way. I think this is probably good advice when learning a new statistical technique, but its importance hadn't really been driven home to me until I did it for this book.
While this book didn't include proofs either, it does include practical and fully worked examples, along with exercises (and a partial solutions manual available online). It's also much shorter, which is a big benefit.
For reading this book for self-study, I'd recommend the following:
1. There are many errors in the book, and it's worth marking up your copy with the errata. Some of the errors are things like critical missing terms in a few key equations or typos in exercises that make them difficult to do.
2. When doing the exercises, many of them can be checked by writing out structural equations and generating a faked data set (e.g. with numpy) by sampling from a distribution that matches the parameters of the problem. Then you know the "right" answer (e.g. how big a particular coefficient is), and you can make sure that your interpretation of the techniques generate an answer that matches it. My reading partner and I found many errors in our solutions this way. I think this is probably good advice when learning a new statistical technique, but its importance hadn't really been driven home to me until I did it for this book.
Shelved as 'to-keep-reference'
November 12, 2021Libro recomendado en el curso Inference on Causal and Structural Parameters using ML and AI
November 3, 2020
In this short book, Pearl gives a broad yet detailed introduction to his flavor of causal inference. That means back-doors and front-doors and graphs as the foundation with potential outcomes and counterfactuals as the fruits to be harvested.
For a scientist, Pearl is an outstandingly good writer. Even his journal articles are readable! His popular book (The Book of Why: The New Science of Cause and Effect) was quite enjoyable and this textbook is concise and clear. I read this book at the same time as I was reading Causal Inference: What If and found that, for the concepts that are covered in both, Pearl's presentation was more clear.
The book has only four chapters. Chapter 1 gives an overview of causal inference and a brief overview of important background from probability theory. Chapter 2 lays out the graphical approach to structural causal models and introduces d-separation. Chapter 3 shows how to connect the graphical models to causal questions, with the central focus being back-door and front-door corrections, including a section on inverse probability weighting and linear models/regression. Chapter 4 expands the computational methods to a wider array of counterfactual questions, ending with extensive examples and explicit formulas for direct and indirect effects under mediation.
The greatest weakness of "The Book of Why" is that the examples are not worked out clearly. After reading it, you are convinced that there is something to this causal inference thing, but you have no intuition as to how to solve even the simplest problem involving confounders or colliders. In that sense, the current book is a worthy sequel. If you follow the equations and exercises (not particularly difficult), you will know how to solve simple causal inference problems.
That raises the question of who this book is intended for. I found the book to be challenging, but not bewildering or unnecessarily complex. I should note that I have a Ph.D. in physics and have worked for several years in something like "data science." In theory the book is intended for undergraduates who are studying "elementary statistics." I guess they would get something out of it, but my guess is that a beginning student would have difficulty appreciating what the relevance of these methods is without familiarity with how things are treated in the absence of them. After all, the math itself is rather simple, comfortably at the level of a precocious undergrad. What makes the subject challenging is understanding how to translate back and forth between assumptions about reality, graphs/equations and numerical estimates.
Unfortunately, there are a large number of typos and other minor errors in the book. He has a corrected pdf on his website if you're interested. Also, the course website is not whatever is written in the text, you need to Google it.
One last point is that there is an ongoing struggle within the causal inference community between Pearl's approach and the Neyman's potential outcomes approach. You'll see it obliquely referenced here, in Hernan's book (from the other side), in sparring journal articles and--of course--on academic Twitter. I kind of wish the argument would be less partisan and more philosophical but I guess even scientists are human beings. To get a sense of what the argument is about, I'd read https://ftp.cs.ucla.edu/pub/stat_ser/...
For a scientist, Pearl is an outstandingly good writer. Even his journal articles are readable! His popular book (The Book of Why: The New Science of Cause and Effect) was quite enjoyable and this textbook is concise and clear. I read this book at the same time as I was reading Causal Inference: What If and found that, for the concepts that are covered in both, Pearl's presentation was more clear.
The book has only four chapters. Chapter 1 gives an overview of causal inference and a brief overview of important background from probability theory. Chapter 2 lays out the graphical approach to structural causal models and introduces d-separation. Chapter 3 shows how to connect the graphical models to causal questions, with the central focus being back-door and front-door corrections, including a section on inverse probability weighting and linear models/regression. Chapter 4 expands the computational methods to a wider array of counterfactual questions, ending with extensive examples and explicit formulas for direct and indirect effects under mediation.
The greatest weakness of "The Book of Why" is that the examples are not worked out clearly. After reading it, you are convinced that there is something to this causal inference thing, but you have no intuition as to how to solve even the simplest problem involving confounders or colliders. In that sense, the current book is a worthy sequel. If you follow the equations and exercises (not particularly difficult), you will know how to solve simple causal inference problems.
That raises the question of who this book is intended for. I found the book to be challenging, but not bewildering or unnecessarily complex. I should note that I have a Ph.D. in physics and have worked for several years in something like "data science." In theory the book is intended for undergraduates who are studying "elementary statistics." I guess they would get something out of it, but my guess is that a beginning student would have difficulty appreciating what the relevance of these methods is without familiarity with how things are treated in the absence of them. After all, the math itself is rather simple, comfortably at the level of a precocious undergrad. What makes the subject challenging is understanding how to translate back and forth between assumptions about reality, graphs/equations and numerical estimates.
Unfortunately, there are a large number of typos and other minor errors in the book. He has a corrected pdf on his website if you're interested. Also, the course website is not whatever is written in the text, you need to Google it.
One last point is that there is an ongoing struggle within the causal inference community between Pearl's approach and the Neyman's potential outcomes approach. You'll see it obliquely referenced here, in Hernan's book (from the other side), in sparring journal articles and--of course--on academic Twitter. I kind of wish the argument would be less partisan and more philosophical but I guess even scientists are human beings. To get a sense of what the argument is about, I'd read https://ftp.cs.ucla.edu/pub/stat_ser/...
June 23, 2019
Although the reader will definitely want to make sure they're reading the latest edition (or at least checking the errata document) to avoid some confusing typos, I found this an excellent introduction to the statistical study of causality. Before reading this book, I'd more or less assumed only randomized controlled trials (or the genetic equivalent) could provide information about the extent to which one variable causes changes in another, as far as statistics goes. Here Pearl offers a lot of tools to do causal analysis on data for which RCTs simply aren't feasible, and when you consider that there are both practical and ethical limitations on our ability to test every hypothesis with an RCT, this is huge.
At the same time, the reasoning behind each formula and technique is transparent, in case you're suspicious that this book is selling snake-oil - and I couldn't blame you for that, as we're all used to thinking of causality as something squarely outside the domain of statistics. It's relatively brief, but it serves its purpose, and cites plenty of resources for those who want more detail, myself included. I admit not every part is crystal clear. Still, if you give the more dense sections an extra read or two, I don't think you'll find anything that is frustratingly inscrutable or hand-wavey (and this is unfortunately rare in mathematical texts, in my experience). For people who need a statistics refresher, the first chapter also provides that, but there's definitely enough content beyond standard undergrad stats classes to satisfy otherwise. Plus there are plenty of connections to realistic examples of policy or medical questions these models can help with.
So yes, I guess I'm drinking the Pearl Kool-aid. This book deserves such praise in my opinion, though, for having the informative lack of fluff of a textbook without the soporific dryness of one.
At the same time, the reasoning behind each formula and technique is transparent, in case you're suspicious that this book is selling snake-oil - and I couldn't blame you for that, as we're all used to thinking of causality as something squarely outside the domain of statistics. It's relatively brief, but it serves its purpose, and cites plenty of resources for those who want more detail, myself included. I admit not every part is crystal clear. Still, if you give the more dense sections an extra read or two, I don't think you'll find anything that is frustratingly inscrutable or hand-wavey (and this is unfortunately rare in mathematical texts, in my experience). For people who need a statistics refresher, the first chapter also provides that, but there's definitely enough content beyond standard undergrad stats classes to satisfy otherwise. Plus there are plenty of connections to realistic examples of policy or medical questions these models can help with.
So yes, I guess I'm drinking the Pearl Kool-aid. This book deserves such praise in my opinion, though, for having the informative lack of fluff of a textbook without the soporific dryness of one.
June 29, 2023
my brain hurts.
July 7, 2021
For the most part an intuitive intro to causal inference. Certain chapters include unnecessary complexity for beginners and the last chapter is a mess.
June 14, 2021
Very beginner-friendly intro to causality. To fully understand the book, you can (1) motivate yourself by visual illustrations of Brady Neal on YouTube, (2) understand important concepts of causal inference by reading the chapters, (3) finish the exercise questions to strengthen your mathematical intuitions of causal models, (4) read recent papers on causal inference at NeurIPS, ICML, ICLR, AISTATS, etc. to understand how frontier researchers apply the concepts and push forward the research; you can also follow Online Causal Inference Seminars to watch talks on newest research.
Key concepts of this book that I recommend to thoroughly understand:
(1) Causality vs. Correlation, as well as independence and conditional independence.
(2) Intervention & the language of Do-Calculus, as well as methods such as adjustment, propensity score matching.
(3) Counterfactuals, as well as social applications of counterfactuals.
Have fun! Causal reasoning can make your model much more robust, transferrable, and teachable for phenomena in the world :)!
Key concepts of this book that I recommend to thoroughly understand:
(1) Causality vs. Correlation, as well as independence and conditional independence.
(2) Intervention & the language of Do-Calculus, as well as methods such as adjustment, propensity score matching.
(3) Counterfactuals, as well as social applications of counterfactuals.
Have fun! Causal reasoning can make your model much more robust, transferrable, and teachable for phenomena in the world :)!
February 15, 2022
I NEVER read a book with so much TYPOS! Errata is almost a complete edition of the book, :( . Everypage has 2 or 3 typos.... I doubt whether this book has been taken seriously by authors.
Details can be found at: http://bayes.cs.ucla.edu/PRIMER --> Errata and updates (last revised: 8.13.2021)
Pros:
1. Enough study questiones with answers, which is really helpful to test our understanding on concepts.
2. Give a shallow blue picture of Causal Diagrams.
Cons:
1. With a statistics background, I still find that this book is a bit rough on narrative and organization.
2. Too much typos make this book hard to dive deeply.
Details can be found at: http://bayes.cs.ucla.edu/PRIMER --> Errata and updates (last revised: 8.13.2021)
Pros:
1. Enough study questiones with answers, which is really helpful to test our understanding on concepts.
2. Give a shallow blue picture of Causal Diagrams.
Cons:
1. With a statistics background, I still find that this book is a bit rough on narrative and organization.
2. Too much typos make this book hard to dive deeply.
July 17, 2019
The almighty statement "Correlation doesn't imply causation!" is becoming more and more cliché nowadays. It does a brilliant job making us believe in nothing and doubt everything. I don't say that this statement is wrong, yet it alone is not enough on the journey to find the truth, the causation.
Let's take an example. What can we say if two variables X and Y are correlated? Maybe X causes Y (even partially). Maybe Y causes X. Or it's also possible that there's a third variable Z that causes both X and Y. Is that it? If those are not the case, can we conclude that this correlation is just a coincidence?
There's at least another interesting case that we should think about, that X and Y both cause Z. In that case, even if X and Y are independent, they are in fact dependent conditioning on Z.
There are not many books, particularly probability & statistics books, tackle this problem. That makes "Causal Inference in Statistics - A Primer" of Pearl, Glymour and Jewell a rare gem. I find this book clear and easy to digest, with illustrative mathematical concepts and examples.
This book, while by no means provides an ultimate answer about the causation of everything, shed bright light for us on this journey. There's a lot to learn, and this book, together with "The Book of Why" of the same author, are a good start.
Let's take an example. What can we say if two variables X and Y are correlated? Maybe X causes Y (even partially). Maybe Y causes X. Or it's also possible that there's a third variable Z that causes both X and Y. Is that it? If those are not the case, can we conclude that this correlation is just a coincidence?
There's at least another interesting case that we should think about, that X and Y both cause Z. In that case, even if X and Y are independent, they are in fact dependent conditioning on Z.
There are not many books, particularly probability & statistics books, tackle this problem. That makes "Causal Inference in Statistics - A Primer" of Pearl, Glymour and Jewell a rare gem. I find this book clear and easy to digest, with illustrative mathematical concepts and examples.
This book, while by no means provides an ultimate answer about the causation of everything, shed bright light for us on this journey. There's a lot to learn, and this book, together with "The Book of Why" of the same author, are a good start.
August 11, 2023
I read this book to learn directly how to measure causal effects from complex causal graphs, despite reading the book of Why. I've realized that I need either very very dimple explanations or incredibly deep ones to understand anything, and The book of Why was half way between. If anyone is legitimately interested in Pearlian Causal inference, this book is SUPERB. It's readable (unlike causality) and technical (unlike the book of why).
Instead of an explicit 1, 2, 3 of what I learned, there's a long list of things that I kind of knew, but now understand. These include: D-separation, the back door criterion, the front door criterion, how to algorithmically determine controls for a known DGP, intuition for controls in IV, and when a path coefficient is estimable for a given DAG when only a subset of variables is measured. There is a lot more that I learned, but I highlight these because of the great depth that this book helped me understand, and now implement in some of my own work (especially what to control for, and how to explicitly define exogenous and endogenous variables en mass).
NOTE: if you're not studying stats at a university, I'd probably not read this lol. Although, I loved it!
Instead of an explicit 1, 2, 3 of what I learned, there's a long list of things that I kind of knew, but now understand. These include: D-separation, the back door criterion, the front door criterion, how to algorithmically determine controls for a known DGP, intuition for controls in IV, and when a path coefficient is estimable for a given DAG when only a subset of variables is measured. There is a lot more that I learned, but I highlight these because of the great depth that this book helped me understand, and now implement in some of my own work (especially what to control for, and how to explicitly define exogenous and endogenous variables en mass).
NOTE: if you're not studying stats at a university, I'd probably not read this lol. Although, I loved it!
October 1, 2023
The books content, the science of causal inference, is nothing short of mesmerizing to me. It made me rethink many concepts in statistics and econometrics. Because it helps enlighten statistics itself at a deeper level, I wish it were taught prior to statistics at universities.
The book is multiple times shorter than the book "Causality" by Pearl. The book is a textbook and is structured like a university course. If you enjoyed "The Book of Why" and want to dive into causal inference or have an econometrics background, this book is a must-work-through.
Two negative points: 1) The book does not put its unique content regarding causal inference in context with other approaches, such as potential outcomes in econometrics. 2) The book is absolutely poorly edited, to the degree that I wonder whether the authors half-assed this in a day or two (which makes the content no less impressive).
The book is multiple times shorter than the book "Causality" by Pearl. The book is a textbook and is structured like a university course. If you enjoyed "The Book of Why" and want to dive into causal inference or have an econometrics background, this book is a must-work-through.
Two negative points: 1) The book does not put its unique content regarding causal inference in context with other approaches, such as potential outcomes in econometrics. 2) The book is absolutely poorly edited, to the degree that I wonder whether the authors half-assed this in a day or two (which makes the content no less impressive).
May 25, 2020
This is a great book that can build a solid theoretical foundation on causal inference. Also, the books provides plenty of examples that helped me understand the practical application of the theories. I especially like the examples with data provided, going through the calculation to understand how incorrect interpretation of the data could lead to completely opposite conclusion is eye opening for me. Highly recommended to readers that want to get a deeper understanding on causal inference.
August 10, 2023
I preferred the Book of Why to this despite it being a longer read. This book is more dense, but I feel like it suffers as a result. Ive personally read dozens of materials that provide a better introduction to DAGs and causal inference than this book. I'm sure all the info is solid though and if you're okay with dense and notation-heavy readings, then this is fine
March 3, 2024
The notations for intervention and counterfactual are very perplexing, making me harder to appreciate the difference between them. Not sure if this is the conventional format in the causal inference community, but it needs a rework IMO.
The author also used many vague and not well-defined terms to explain concepts, which only makes this introductory book harder to read.
The author also used many vague and not well-defined terms to explain concepts, which only makes this introductory book harder to read.
August 8, 2020
The advantage of this one is it's really short compared with the "Causality". The main idea is transform the probability of hypothetic problem into the probability you've got. So finally the quality of data is very very important.
August 21, 2023
An easy to read short intro to causal inference that introduces backdoors, frontdoors, propensity weighting and counterfactuals.
My only real criticism is how they talk about linear systems: as if they truly are linear rather than approximately linear in the regime of interest (most cases).
My only real criticism is how they talk about linear systems: as if they truly are linear rather than approximately linear in the regime of interest (most cases).
September 19, 2019
Very concise, to the point overview. Gives the basic understanding of the building components in the field. Also makes much easier to understand more advanced literature on this topic.
Want to read
October 13, 2021Página en
http://bayes.cs.ucla.edu/PRIMER/
http://bayes.cs.ucla.edu/PRIMER/
May 12, 2022
Amazing book! Got lost halfway through but persisted and finished it because it was so cool.
September 16, 2022
More abstract than I expect.
The book is well structured and organised.
I read the book and refer to an online YouTube channel by Brady Neal (a Mila PHD), free course.
The book is well structured and organised.
I read the book and refer to an online YouTube channel by Brady Neal (a Mila PHD), free course.
November 23, 2022
Rather abstract overview of causal inference and statistical methods.
Read
April 18, 2024Needed more romance
Shelved as 'paused-reading'
November 23, 2023Apparently there are quite a few major typos that substantively affect the content. I need to mark the errata in my copy of the book before I read it...
Also, another review links to an article "Does Obesity Shorten Life? Or is it the Soda? On Non-manipulable Causes", intending to illustrate how Pearl's book differs from others like Hernan's. Apparently there is a big "ongoing struggle within the causal inference community between Pearl's approach and the Neyman's potential outcomes approach." I haven't read this Pearl book yet but I did read the article, and whoo boy, I was not impressed. In that article, Pearl sounds like he is full of nonsense, dismissing valid concerns with handwavy arguments and meaningless abstractions.
Also, another review links to an article "Does Obesity Shorten Life? Or is it the Soda? On Non-manipulable Causes", intending to illustrate how Pearl's book differs from others like Hernan's. Apparently there is a big "ongoing struggle within the causal inference community between Pearl's approach and the Neyman's potential outcomes approach." I haven't read this Pearl book yet but I did read the article, and whoo boy, I was not impressed. In that article, Pearl sounds like he is full of nonsense, dismissing valid concerns with handwavy arguments and meaningless abstractions.
March 10, 2020
A pithy introduction to Causal Inference. This book is extremely information dense. Every sentence serves a purpose. Pearl can be subtle at times and his intelligence shines through. I walked away with a working understanding of Causal Inference. I think this is a great first read before academic papers.
Displaying 1 - 25 of 25 reviews