Causality: Model, Reasoning, and Inference

【负责】周浩杰，如有问题，欢迎交流与提出建议

【说明】本书无中文版，故目录内容是自己翻译的，所看的是英文第二版

书籍简介

这本书是因果科学领域最著名的学者之一朱迪亚·珀尔所著。它深入讨论了当代的因果分析方法，将因果科学从一个模糊的概念变成一个可以量化的理论，并可以广泛应用于数理统计、人工智能、经济学、认知科学等领域。

基本信息

• 书名 因果：模型、推理和推论 Causality: Model, Reasoning, and Inference 2nd edition
• 作者 朱迪亚·珀尔 Judea Pearl
• 出版社 剑桥大学出版社
• 出版年份 2009
• 在线网站 含有习题、勘误、问题讨论等资源

目录与概要

1 概率、图和因果模型介绍  Introduction to Probabilities, Graphs, and Causal Models 1

1.1 概率论介绍  Introduction to Probability Theory 1

1.1.1 为什么需要概率 Why Probabilities? 1

• 因果论断的发生具有不确定性，比如“心不在焉的开车会导致车祸”，前因会让后果更容易发生，但不是绝对的。
• 与断言逻辑相比，基于概率的表达更容易处理，不然断言需要考虑到大量使其不成立的特例。

1.1.2 概率论中的基本概念 Basic Concepts in Probability Theory 2

• 介绍有关概率论中离散变量的相关基础知识，并聚焦于贝叶斯推理的角度。

1.1.3 Combining Predictive and Diagnostic Supports 6

1.1.4 随机变量与数学期望 Random Variables and Expectations 8

1.1.5 条件独立与Graphoid Conditional Independence and Graphoids 11

1.2 图和概率  Graphs and Probabilities 12

1.2.1 图的记号与术语 Graphical Notation and Terminology 12

1.2.2 贝叶斯网络 Bayesian Networks 13

1.2.3 d-分离准则 The d-Separation Criterion 16

1.2.4 贝叶斯网络推断 Inference with Bayesian Networks 20

1.3 因果贝叶斯网络 Causal Bayesian Networks 21

1.3.1 Causal Networks as Oracles for Interventions 22

1.3.2 Causal Relationships and Their Stability 24

1.4 Functional Causal Models 26

1.4.1 Structural Equations 27

1.4.2 Probabilistic Predictions in Causal Models 30

1.4.3 Interventions and Causal Effects in Functional Models 32

1.4.4 Counterfactuals in Functional Models 33

1.5 Causal versus Statistical Terminology 38

2 推断因果理论  A Theory of Inferred Causation 41

2.1 介绍—基本的直觉 Introduction – The Basic Intuitions 42

2.2 因果发现框架 The Causal Discovery Framework 43

2.3 模型偏好（奥卡姆剃刀） Model Preference (Occam's Razor) 45

2.4 稳定分布 Stable Distributions 48

2.5 发现DAG结构 Recovering DAG Structures 49

2.6 滞后结构再发现 Recovering Latent Structures 51

2.7 因果关系推断的局部准则 Local Criteria for Inferring Causal Relations 54

2.8 Nontemporal Causation and Statistical Time 57

2.9 总结 Conclusions 59

2.9.1 On Minimality, Markov, and Stability 61

3 Causal Diagrams and the Identification of Causal Effects 65

3.1 Introduction 66

3.2 Intervention in Markovian Models 68

3.2.1 Graphs as Models of Interventions 68

3.2.2 Interventions as Variables 70

3.2.3 Computing the Effect of Interventions 72

3.2.4 Identification of Causal Quantities 77

3.3 Controlling Confounding Bias 78

3.3.1 The Back-Door Criterion 79

3.3.2 The Front-Door Criterion 81

3.3.3 Example: Smoking and the Genotype Theory 83

3.4 A Calculus of Intervention 85

3.4.1 Preliminary Notation 85

3.4.2 Inference Rules 85

3.4.3 Symbolic Derivation of Causal Effects: An Example 86

3.4.4 Causal Inference by Surrogate Experiments 88

3.5 Graphical Tests of Identifiability 89

3.5.1 Identifying Models 91

3.5.2 Nonidentifying Models 93

3.6 Discussion 94

3.6.1 Qualifications and Extensions 94

3.6.2 Diagrams as a Mathematical Language 96

3.6.3 Translation from Graphs to Potential Outcomes 98

3.6.4 Relations to Robins’s G-Estimation 102

4 Actions, Plans, and Direct Effects 107

4.1 Introduction 108

4.1.1 Actions, Acts, and Probabilities 108

4.1.2 Actions in Decision Analysis 110

4.1.3 Actions and Counterfactuals 112

4.2 Conditional Actions and Stochastic Policies 113

4.3 When Is the Effect of an Action Identifiable? 114

4.3.1 Graphical Conditions for Identification 114

4.3.2 Remarks on Efficiency 116

4.3.3 Deriving a Closed-Form Expression for Control Queries 117

4.3.4 Summary 118

4.4 The Identification of Dynamic Plans 118

4.4.1 Motivation 118

4.4.2 Plan Identification: Notation and Assumptions 120

4.4.3 Plan Identification: The Sequential Back-Door Criterion 121

4.4.4 Plan Identification: A Procedure 124

4.5 Direct and Indirect Effects 126

4.5.1 Direct versus Total Effects 126

4.5.2 Direct Effects, Definition, and Identification 127

4.5.3 Example: Sex Discrimination in College Admission 128

4.5.4 Natural Direct Effects 130

4.5.5 Indirect Effects and the Mediation Formula 132

5 Causality and Structural Models in Social Science and Economics 133

5.1 Introduction 134

5.1.1 Causality in Search of a Language 134

5.1.2 SEM: How Its Meaning Became Obscured 135

5.1.3 Graphs as a Mathematical Language 138

5.2 Graphs and Model Testing 140

5.2.1 The Testable Implications of Structural Models 140

5.2.2 Testing the Testable 144

5.2.3 Model Equivalence 145

5.3 Graphs and Identifiability 149

5.3.1 Parameter Identification in Linear Models 149

5.3.2 Comparison to Nonparametric Identification 154

5.3.3 Causal Effects: The Interventional Interpretation of Structural Equation Models 157

5.4 Some Conceptual Underpinnings 159

5.4.1 What Do Structural Parameters Really Mean? 159

5.4.2 Interpretation of Effect Decomposition 163

5.4.3 Exogeneity, Superexogeneity, and Other Frills 165

5.5 Conclusion 170

5.6 Postscript for the Second Edition 171

5.6.1 An Econometric Awakening?   171

5.6.2 Identification in Linear Models  171

5.6.3 Robustness of Causal Claims  172

6 Simpson’s Paradox, Confounding, and Collapsibility 173

6.1 Simpson’s Paradox: An Anatomy 174

6.1.1 A Tale of a Non-Paradox 174

6.1.2 A Tale of Statistical Agony 175

6.1.3 Causality versus Exchangeability 177

6.1.4 A Paradox Resolved (Or: What Kind of Machine Is Man?) 180

6.2 Why There Is No Statistical Test for Confounding, Why Many Think There Is, and Why They Are Almost Right 182

6.2.1 Introduction 182

6.2.2 Causal and Associational Definitions 184

6.3 How the Associational Criterion Fails 185

6.3.1 Failing Sufficiency via Marginality 185

6.3.2 Failing Sufficiency via Closed-World Assumptions 186

6.3.3 Failing Necessity via Barren Proxies 186

6.3.4 Failing Necessity via Incidental Cancellations 188

6.4 Stable versus Incidental Unbiasedness 189

6.4.1 Motivation 189

6.4.2 Formal Definitions 191

6.4.3 Operational Test for Stable No-Confounding 192

6.5 Confounding, Collapsibility, and Exchangeability 193

6.5.1 Confounding and Collapsibility 193

6.5.2 Confounding versus Confounders 194

6.5.3 Exchangeability versus Structural Analysis of Confounding 196

6.6 Conclusions 199

7 The Logic of Structure-Based Counterfactuals 201

7.1 Structural Model Semantics 202

7.1.1 Definitions: Causal Models, Actions, and Counterfactuals 202

7.1.2 Evaluating Counterfactuals: Deterministic Analysis 207

7.1.3 Evaluating Counterfactuals: Probabilistic Analysis 212

7.1.4 The Twin Network Method 213

7.2 Applications and Interpretation of Structural Models 215

7.2.1 Policy Analysis in Linear Econometric Models: An Example 215

7.2.2 The Empirical Content of Counterfactuals 217

7.2.3 Causal Explanations, Utterances, and Their Interpretation 221

7.2.4 From Mechanisms to Actions to Causation 223

7.2.5 Simon’s Causal Ordering 226

7.3 Axiomatic Characterization 228

7.3.1 The Axioms of Structural Counterfactuals 228

7.3.2 Causal Effects from Counterfactual Logic: An Example 231

7.3.3 Axioms of Causal Relevance 234

7.4 Structural and Similarity-Based Counterfactuals 238

7.4.1 Relations to Lewis’s Counterfactuals 238

7.4.2 Axiomatic Comparison 240

7.4.3 Imaging versus Conditioning 242

7.4.4 Relations to the Neyman–Rubin Framework 243

7.4.5 Exogeneity and Instruments: Counterfactual and Graphical Definitions 245

7.5 Structural versus Probabilistic Causality 249

7.5.1 The Reliance on Temporal Ordering 249

7.5.2 The Perils of Circularity 250

7.5.3 Challenging the Closed-World Assumption, with Children 252

7.5.4 Singular versus General Causes 253

7.5.5 Summary 256

8 Imperfect Experiments: Bounding Effects and Counterfactuals 259

8.1 Introduction 259

8.1.1 Imperfect and Indirect Experiments 259

8.1.2 Noncompliance and Intent to Treat 261

8.2 Bounding Causal Effects with Instrumental Variables  262

8.2.1 Problem Formulation: Constrained Optimization 262

8.2.2 Canonical Partitions: The Evolution of Finite-Response Variables 263

8.2.3 Linear Programming Formulation 266

8.2.4 The Natural Bounds 268

8.2.5 Effect of Treatment on the Treated (ETT) 269

8.2.6 Example: The Effect of Cholestyramine 270

8.3 Counterfactuals and Legal Responsibility 271

8.4 A Test for Instruments 274

8.5 A Bayesian Approach to Noncompliance 275

8.5.1 Bayesian Methods and Gibbs Sampling 275

8.5.2 The Effects of Sample Size and Prior Distribution 277

8.5.3 Causal Effects from Clinical Data with Imperfect Compliance 277

8.5.4 Bayesian Estimate of Single-Event Causation 280

8.6 Conclusion 281

9 Probability of Causation: Interpretation and Identification 283

9.1 Introduction 283

9.2 Necessary and Sufficient Causes: Conditions of Identification 286

9.2.1 Definitions, Notation, and Basic Relationships 286

9.2.2 Bounds and Basic Relationships under Exogeneity 289

9.2.3 Identifiability under Monotonicity and Exogeneity 291

9.2.4 Identifiability under Monotonicity and Nonexogeneity 293

9.3 Examples and Applications 296

9.3.1 Example 1: Betting against a Fair Coin 296

9.3.2 Example 2: The Firing Squad 297

9.3.3 Example 3: The Effect of Radiation on Leukemia 299

9.3.4 Example 4: Legal Responsibility from Experimental and Nonexperimental Data 302

9.3.5 Summary of Results 303

9.4 Identification in Nonmonotonic Models 304

9.5 Conclusions 307

10 The Actual Cause 309

10.1 Introduction: The Insufficiency of Necessary Causation 309

10.1.1 Singular Causes Revisited 309

10.1.2 Preemption and the Role of Structural Information 311

10.1.3 Overdetermination and Quasi-Dependence 313

10.1.4 Mackie's INUS Condition 313

10.2 Production, Dependence, and Sustenance 316

10.3 Causal Beams and Sustenance-Based Causation 318

10.3.1 Causal Beams: Definitions and Implications 318

10.3.2 Examples: From Disjunction to General Formulas 320

10.3.3 Beams, Preemption, and the Probability of Single-Event Causation 322

10.3.4 Path-Switching Causation 324

10.3.5 Temporal Preemption 325

10.4 Conclusions 327

11 Reflections, Elaborations, and Discussions with Readers 331

11.1 Causal, Statistical, and Graphical Vocabulary  331

11.1.1 Is the Causal-Statistical Dichotomy Necessary?  331

11.1.2 d-Separation without Tears (Chapter 1, pp. 16–18)  335

11.2 Reversing Statistical Time (Chapter 2, p. 58–59)  337

11.3 Estimating Causal Effects  338

11.3.1 The Intuition behind the Back-Door Criterion (Chapter 3, p. 79)  338

11.3.2 Demystifying “Strong Ignorability” 341

11.3.3 Alternative Proof of the Back-Door Criterion  344

11.3.4 Data vs. Knowledge in Covariate Selection  346

11.3.5 Understanding Propensity Scores  348

11.3.6 The Intuition behind do-Calculus  352

11.3.7 The Validity of G-Estimation  352

11.4 Policy Evaluation and the do-Operator  354

11.4.1 Identifying Conditional Plans (Section 4.2, p. 113)  354

11.4.2 The Meaning of Indirect Effects  355

11.4.3 Can do(x) Represent Practical Experiments?  358

11.4.4 Is the do(x) Operator Universal?  359

11.4.5 Causation without Manipulation!!!   361

11.4.6 Hunting Causes with Cartwright  362

11.4.7 The Illusion of Nonmodularity  364

11.5 Causal Analysis in Linear Structural Models  366

11.5.1 General Criterion for Parameter Identification (Chapter 5, pp. 149–54)  366

11.5.2 The Causal Interpretation of Structural Coefficients  366

11.5.3 Defending the Causal Interpretation of SEM (or, SEM Survival Kit)  368

11.5.4 Where Is Economic Modeling Today? – Courting Causes with Heckman  374

11.5.5 External Variation versus Surgery  376

11.6 Decisions and Confounding (Chapter 6)  380

11.6.1 Simpson's Paradox and Decision Trees  380

11.6.2 Is Chronological Information Sufficient for Decision Trees?  382

11.6.3 Lindley on Causality, Decision Trees, and Bayesianism  384

11.6.4 Why Isn't Confounding a Statistical Concept?  387

11.7 The Calculus of Counterfactuals  389

11.7.1 Counterfactuals in Linear Systems  389

11.7.2 The Meaning of Counterfactuals  391

11.7.3 d-Separation of Counterfactuals  393

11.8 Instrumental Variables and Noncompliance  395

11.8.1 Tight Bounds under Noncompliance   395

11.9 More on Probabilities of Causation  396

11.9.1 Is "Guilty with Probability One" Ever Possible?  396

11.9.2 Tightening the Bounds on Probabilities of Causation  398