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

【备注】好难，有些内容理解的不深刻因而写的不太好，我只能抛砖引玉，需要更厉害的人在初版基础上进一步迭代

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 因果论：模型、推理和推断 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，并主要聚焦于贝叶斯推理。

1.1.3 组合预测支持和诊断支持 【感觉翻译的不好，但又不知道怎么翻译的更好，只能直译】Combining Predictive and Diagnostic Supports 6

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

• 介绍了随机变量的符号表示，单离散变量的数学期望，条件期望，函数期望，方差。
• 双变量的数学期望，相关系数，条件相关系数以及单连续变量的概率密度函数。

1.1.5 条件独立与Graphoid Conditional Independence and Graphoids 11

• 介绍了条件独立的定义以及5个性质，对称，消去，弱连接，合并与插入。
• 这些性质被称作graphoid公理，并在书中给出了直观解释。

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

• 结点，边，邻边，路径，DAG，根节点，树，链，完全图

1.2.2 贝叶斯网络 Bayesian Networks 13

• 介绍了马尔可夫父代的定义，这有利于简化贝叶斯模型的输入信息，以及马尔可夫相容性的定义。

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

• d-分离的定义，以及概率下的d-分离，有序马尔可夫条件，父代马尔可夫条件，观测等价性这些定理。

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 作为Oracle的被干预的因果网络 Causal Networks as Oracles for Interventions 22

• 因果贝叶斯网络的定义和两个性质

1.3.2 因果关系及其稳定性 Causal Relationships and Their Stability 24

• 说明了因果关系为何比概率关系稳定，因果关系的重要性。

1.4 函数因果模型 Functional Causal Models 26

1.4.1 结构等式 Structural Equations 27

1.4.2 因果模型中的概率预测 Probabilistic Predictions in Causal Models 30

• 介绍了因果马尔可夫条件，其通过父代马尔科夫条件建立了因果和概率间的联系

1.4.3 函数模型中的干预和因果效应 Interventions and Causal Effects in Functional Models 32

• 阐释了为什么干预在函数模型中的表示比在随机模型更灵活和通用

1.4.4 函数模型中的反事实 Counterfactuals in Functional Models 33

• 强调了回答反事实问题是困难的，说明了反事实和结构等式间的关系，随机因果模型不足以计算反事实中概率的真正原因。

1.5 因果和统计学的术语 Causal versus Statistical Terminology 38

• 介绍了概率参数，统计参数，因果参数，统计假设与因果假设。
• 对比了统计学与因果科学术语的差异

2 因果推断理论  A Theory of Inferred Causation 41

2.1 绪论：直观的理解 Introduction – The Basic Intuitions 42

2.2 因果发现框架 The Causal Discovery Framework 43

• 因果模型和因果结构的定义

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

• 由于符合条件的模型有很多，通过最小化确定模型
• 介绍了推断因果（初级），潜在结构，结构偏好，最小性，一致性，推断因果这些概念的定义

2.4 稳定分布 Stable Distributions 48

• 为什么需要提出稳定性这个概念。最小性原则不能保证模型是最小的或是计算可行的【看着有点怪，具体最小是什么意思我也不是非常懂，这句话的意思出自这里Although the minimality principle is sufficient for forming a normative theory of inferred causation, it does not guarantee that the structure of the actual data-generating model would be minimal, or that the search through the vast space of minimal structures would be computationally practical】
• 介绍稳定性的定义，阐释其与最小性间的关系

2.5 发现DAG结构 Recovering DAG Structures 49

• IC算法，输入稳定概率分布，输出等价DAG结构

2.6 发现隐结构 Recovering Latent Structures 51

• 投影的定义，Verma定理，任何隐结构至少有一个投影，识别不同特点边的IC*算法

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

• 潜在因果，真实因果，伪相关，有时间信息的真实因果，有时间信息的伪相关这些概念的定义

2.8 非时间因果与统计时间 Nontemporal Causation and Statistical Time 57

2.9 总结 Conclusions 59

2.9.1 关于极小性，马尔可夫性和稳定性 On Minimality, Markov, and Stability 61

3 因果图和识别因果效应 Causal Diagrams and the Identification of Causal Effects 65

3.1 简介 Introduction 66

3.2 马尔可夫模型中的干预 Intervention in Markovian Models 68

3.2.1 作为干预模型的图 Graphs as Models of Interventions 68

3.2.2 作为干预的变量 Interventions as Variables 70

3.2.3 计算干预的效应 Computing the Effect of Interventions 72

3.2.4 识别因果量值 Identification of Causal Quantities 77

3.3 控制混杂偏差 Controlling Confounding Bias 78

3.3.1 后门准则 The Back-Door Criterion 79

3.3.2 前门准则 The Front-Door Criterion 81

3.3.3 例子：吸烟和基因论 Example: Smoking and the Genotype Theory 83

3.4 计算干预 A Calculus of Intervention 85

3.4.1 记号预备 Preliminary Notation 85

3.4.2 推理规则 Inference Rules 85

3.4.3 例子：因果效应的符号推导 Symbolic Derivation of Causal Effects: An Example 86

3.4.4 替代试验的因果推断 Causal Inference by Surrogate Experiments 88

• 由于一些原因如成本或伦理问题，不能控制某变量进行实验，于是需要控制另一个可替代的变量
• 介绍利用替代变量进行因果效应的计算方法

3.5 可识别性的图测试 Graphical Tests of Identifiability 89

3.5.1 可识别模型 Identifying Models 91

3.5.2 不可识别模型 Nonidentifying Models 93

3.6 讨论 Discussion 94

3.6.1 要求与扩展 Qualifications and Extensions 94

3.6.2 作为数学语言的图 Diagrams as a Mathematical Language 96

3.6.3 从图到潜在因果的转换 Translation from Graphs to Potential Outcomes 98

3.6.4 跟Robin的G-估计的关系 Relations to Robins's G-Estimation 102

4 行动，计划和直接效应 Actions, Plans, and Direct Effects 107

4.1 简介 Introduction 108

4.1.1 行动，动作和概率 Actions, Acts, and Probabilities 108

4.1.2 决策分析中的行动 Actions in Decision Analysis 110

4.1.3 行动和反事实 Actions and Counterfactuals 112

4.2 有条件行动和随机策略 Conditional Actions and Stochastic Policies 113

4.3 什么时候行动的结果是可测量的 When Is the Effect of an Action Identifiable? 114

4.3.1 基于图的识别条件 Graphical Conditions for Identification 114

4.3.2 识别效率 Remarks on Efficiency 116

4.3.3 对控制问题解析解的推到 Deriving a Closed-Form Expression for Control Queries 117

4.3.4 总结 Summary 118

4.4 动态计划的识别 The Identification of Dynamic Plans 118

4.4.1 动机 Motivation 118

4.4.2 识别计划：记号和假设 Plan Identification: Notation and Assumptions 120

4.4.3 识别计划：顺序后门准则 Plan Identification: The Sequential Back-Door Criterion 121

4.4.4 识别计划：流程 Plan Identification: A Procedure 124

4.5 直接和间接效应 Direct and Indirect Effects 126

4.5.1 直接效应和总效应 Direct versus Total Effects 126

4.5.2 直接效益，定义和识别 Direct Effects, Definition, and Identification 127

4.5.3 例子：大学录取中的性别歧视 Example: Sex Discrimination in College Admission 128

4.5.4 自然直接效应 Natural Direct Effects 130

4.5.5 间接效应和中介公式 Indirect Effects and the Mediation Formula 132

5 社会学和经济学中的因果关系和结构模型 Causality and Structural Models in Social Science and Economics 133

5.1 简介 Introduction 134

5.1.1 寻找因果语言 Causality in Search of a Language 134

5.1.2 SEM：意思是怎么变模糊的 SEM: How Its Meaning Became Obscured 135

5.1.3 作为数学语言的图 Graphs as a Mathematical Language 138

5.2 图和模型测试 Graphs and Model Testing 140

5.2.1 结构模型的可检验含义 The Testable Implications of Structural Models 140

5.2.2 检验和可检验性 Testing the Testable 144

5.2.3 模型等价 Model Equivalence 145

5.3 图和可识别性 Graphs and Identifiability 149

5.3.1 线性模型的参数识别 Parameter Identification in Linear Models 149

5.3.2 对比非参数识别 Comparison to Nonparametric Identification 154

5.3.3 因果效应：结构等式模型的干预解释 Causal Effects: The Interventional Interpretation of Structural Equation Models 157

5.4 部分基础概念 Some Conceptual Underpinnings 159

5.4.1 结构参数的真正含义是什么？ What Do Structural Parameters Really Mean? 159

5.4.2 效应分解的解释 Interpretation of Effect Decomposition 163

5.4.3 外生性，超外生性和其他 Exogeneity, Superexogeneity, and Other Frills 165

5.5 结论 Conclusion 170

5.6 第二版附言 Postscript for the Second Edition 171

5.6.1 计量经济学的觉醒 An Econometric Awakening?   171

5.6.2 线性模型的识别问题 Identification in Linear Models  171

5.6.3 因果论断的鲁棒性 Robustness of Causal Claims  172

6 辛普森悖论，混杂与可压缩性 Simpson's Paradox, Confounding, and Collapsibility 173

6.1 剖析辛普森悖论 Simpson's Paradox: An Anatomy 174

6.1.1 一个有关悖论的示例 A Tale of a Non-Paradox 174

6.1.2 统计学中苦恼的事情 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