Causal Inference in Statistics: A Primer
__Judea Pearl, Computer Science and Statistics, University of California Los Angeles, USA__
__Madelyn Glymour, Philosophy, Carnegie Mellon University, Pittsburgh, USA__
and
__Nicholas P. Jewell, Biostatistics, University of California, Berkeley, USA__
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.

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lgli/M_Mathematics/MV_Probability/MVsa_Statistics and applications/Pearl J., Glymour M., Jewell N.P. Causal inference in statistics.. a primer (Wiley, 2016)(ISBN 9781119186847)(O)(159s)_MVsa_.pdf

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

John Wiley & Sons, Incorporated

American Geophysical Union

Wiley-Blackwell

Wiely

Wiley Blackwell Higher Education, Chichester, West Sussex, UK, 2016

Reprint with revisions, Chichester, 2019

United States, United States of America

0

lg1455171

producers:
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Cover 1
Title Page 5
Copyright 6
Dedication 7
Contents 9
About the Authors 11
Preface 13
List of Figures 17
About the Companion Website 21
Chapter 1 Preliminaries: Statistical and Causal Models 23
1.1 Why Study Causation 23
1.2 Simpsons Paradox 23
1.3 Probability and Statistics 29
1.3.1 Variables 29
1.3.2 Events 30
1.3.3 Conditional Probability 30
1.3.4 Independence 32
1.3.5 Probability Distributions 33
1.3.6 The Law of Total Probability 33
1.3.7 Using Bayes Rule 35
1.3.8 Expected Values 38
1.3.9 Variance and Covariance 39
1.3.10 Regression 42
1.3.11 Multiple Regression 44
1.4 Graphs 46
1.5 Structural Causal Models 48
1.5.1 Modeling Causal Assumptions 48
1.5.2 Product Decomposition 51
Chapter 2 Graphical Models and Their Applications 57
2.1 Connecting Models to Data 57
2.2 Chains and Forks 57
2.3 Colliders 62
2.4 d-separation 67
2.5 Model Testing and Causal Search 70
Chapter 3 The Effects of Interventions 75
3.1 Interventions 75
3.2 The Adjustment Formula 77
3.2.1 To Adjust or not to Adjust? 80
3.2.2 Multiple Interventions and the Truncated Product Rule 82
3.3 The Backdoor Criterion 83
3.4 The Front-Door Criterion 88
3.5 Conditional Interventions and Covariate-Specific Effects 92
3.6 Inverse Probability Weighing 94
3.7 Mediation 97
3.8 Causal Inference in Linear Systems 100
3.8.1 Structural versus Regression Coefficients 102
3.8.2 The Causal Interpretation of Structural Coefficients 103
3.8.3 Identifying Structural Coefficients and Causal Effect 105
3.8.4 Mediation in Linear Systems 109
Chapter 4 Counterfactuals and Their Applications 111
4.1 Counterfactuals 111
4.2 Defining and Computing Counterfactuals 113
4.2.1 The Structural Interpretation of Counterfactuals 113
4.2.2 The Fundamental Law of Counterfactuals 115
4.2.3 From Population Data to Individual Behavior-An Illustration 116
4.2.4 The Three Steps in Computing Counterfactuals 118
4.3 Nondeterministic Counterfactuals 120
4.3.1 Probabilities of Counterfactuals 120
4.3.2 The Graphical Representation of Counterfactuals 123
4.3.3 Counterfactuals in Experimental Settings 125
4.3.4 Counterfactuals in Linear Models 128
4.4 Practical Uses of Counterfactuals 129
4.4.1 Recruitment to a Program 129
4.4.2 Additive Interventions 131
4.4.3 Personal Decision Making 133
4.4.4 Sex Discrimination in Hiring 135
4.4.5 Mediation and Path-disabling Interventions 136
4.5 Mathematical Tool Kits for Attribution and Mediation 138
4.5.1 A Tool Kit for Attribution and Probabilities of Causation 138
4.5.2 A Tool Kit for Mediation 142
References 149
Index 155
EULA 159

Causal Inference in Statistics: A Primer Judea Pearl, Computer Science and Statistics, University of California Los Angeles, USA Madelyn Glymour, Philosophy, Carnegie Mellon University, Pittsburgh, USA and Nicholas P. Jewell, Biostatistics, University of California, Berkeley, USA 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, "Dus 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

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.--book Cover Preliminaries : Statistical And Causal Models -- Graphical Models And Their Applications -- The Effects Of Interventions -- Counterfactuals And Their Applications. Judea Pearl, Madelyn Glymour, Nicholas Jewell. Includes Bibliographical References And Index.

2016-03-06