Causal Inference in Statistics A Primer

by Pearl, Judea; Glymour, Madelyn; Jewell, Nicholas P.

• ISBN13: 9781119186847
• ISBN10: 1119186846
• Edition: 1st
• Format: Paperback
• Copyright: 2016-03-07
• Publisher: Wiley

Summary

CAUSAL INFERENCE IN STATISTICS

A Primer

Causality 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.

Author Biography

Judea Pearl is Professor of Computer Science and Statistics at the University of California, Los Angeles, where he directs the Cognitive Systems Laboratory and conducts research in artificial intelligence, causal inference and philosophy of science. He is a Co-Founder and Editor of the Journal of Causal Inference and the author of three landmark books in inference-related areas. His latest book, Causality: Models, Reasoning and Inference (Cambridge, 2000, 2009), has introduced many of the methods used in modern causal analysis. It  won the Lakatosh Award from the London School of Economics and is cited by more than 10,000 scientific publications.

Pearl is a member of the National Academy of Sciences, the National Academy of Engi­neering , and a Founding Fellow of the Association for Artificial Intelligence. He is a recipient of numerous prizes and awards, including the Technion's Harvey Prize and the ACM Alan Turing Award for fundamental contributions  to probabilistic and causal reasoning.

Madelyn Glymour is a data analyst at Carnegie Mellon University, and a science writer and editor for the Cognitive Systems Laboratory at UCLA. Her interests lie in causal discovery and in the art of making complex concepts accessible to broad audiences.

Nicholas P. Jewell is Professor of Biostatistics and Statistics at the University of California, Berkeley. He has held various academic and administrative positions at Berkeley since his arrival in 1981, most notably serving as Vice Provost from 1994 to 2000. He has also held academic appointments at the University of Edinburgh, Oxford University, the London School of Hygiene and Tropical Medicine, and at the University of Kyoto. In 2007, he was a Fellow at the Rockefeller Foundation Bellagio Study Center in Italy.

Jewell  is a Fellow  of the American  Statistical  Association,  the Institute of  Mathematical Statistics, and the American Association for the Advancement of Science (AAAS). He is a past winner of the Snedecor Award and the Marvin Zelen Leadership Award in Statistical Science from Harvard University. He is currently the Editor of the Journal of the American Statistical Association - Theory & Methods , and Chair of the Statistics Section of AAAS. His research focuses on the application of statistical methods to infectious and chronic disease epidemiology, the assessment of drug safety, time-to-event analyses, and human rights.

Videos: 

Introduction to Causality – Part I with Professors Judea Pearl and Nicholas P. Jewell

Teaching Causality – Part I with Professors Judea Pearl and Rob Gould

In order to access Part II for each of these videos, please register with Statistics Views for free

 

Table of Contents

About the Authors ix

Preface xi

List of Figures xv

About the Companion Website xix

1 Preliminaries: Statistical and Causal Models 1

1.1 Why Study Causation 1

1.2 Simpson’s Paradox 1

1.3 Probability and Statistics 7

1.3.1 Variables 7

1.3.2 Events 8

1.3.3 Conditional Probability 8

1.3.4 Independence 10

1.3.5 Probability Distributions 11

1.3.6 The Law of Total Probability 11

1.3.7 Using Bayes’ Rule 13

1.3.8 Expected Values 16

1.3.9 Variance and Covariance 17

1.3.10 Regression 20

1.3.11 Multiple Regression 22

1.4 Graphs 24

1.5 Structural Causal Models 26

1.5.1 Modeling Causal Assumptions 26

1.5.2 Product Decomposition 29

2 Graphical Models and Their Applications 35

2.1 Connecting Models to Data 35

2.2 Chains and Forks 35

2.3 Colliders 40

2.4 d-separation 45

2.5 Model Testing and Causal Search 48

3 The Effects of Interventions 53

3.1 Interventions 53

3.2 The Adjustment Formula 55

3.2.1 To Adjust or not to Adjust? 58

3.2.2 Multiple Interventions and the Truncated Product Rule 60

3.3 The Backdoor Criterion 61

3.4 The Front-Door Criterion 66

3.5 Conditional Interventions and Covariate-Specific Effects 70

3.6 Inverse Probability Weighing 72

3.7 Mediation 75

3.8 Causal Inference in Linear Systems 78

3.8.1 Structural versus Regression Coefficients 80

3.8.2 The Causal Interpretation of Structural Coefficients 81

3.8.3 Identifying Structural Coefficients and Causal Effect 83

3.8.4 Mediation in Linear Systems 87

4 Counterfactuals and Their Applications 89

4.1 Counterfactuals 89

4.2 Defining and Computing Counterfactuals 91

4.2.1 The Structural Interpretation of Counterfactuals 91

4.2.2 The Fundamental Law of Counterfactuals 93

4.2.3 From Population Data to Individual Behavior – An Illustration 94

4.2.4 The Three Steps in Computing Counterfactuals 96

4.3 Nondeterministic Counterfactuals 98

4.3.1 Probabilities of Counterfactuals 98

4.3.2 The Graphical Representation of Counterfactuals 101

4.3.3 Counterfactuals in Experimental Settings 103

4.3.4 Counterfactuals in Linear Models 106

4.4 Practical Uses of Counterfactuals 107

4.4.1 Recruitment to a Program 107

4.4.2 Additive Interventions 109

4.4.3 Personal Decision Making 111

4.4.4 Sex Discrimination in Hiring 113

4.4.5 Mediation and Path-disabling Interventions 114

4.5 Mathematical Tool Kits for Attribution and Mediation 116

4.5.1 A Tool Kit for Attribution and Probabilities of Causation 116

4.5.2 A Tool Kit for Mediation 120

References 127

Index 133