134
个编辑
更改
跳到导航
跳到搜索
小第15行：
第15行： + − # '''概率、图和因果模型介绍 Introduction to Probabilities, Graphs, and Causal Models''' + − ## 概率论介绍 Introduction to Probability Theory − ### 为什么需要概率 Why Probabilities? − ### 概率论的基本概念 Basic Concepts in Probability Theory − ### Combining Predictive and Diagnostic Supports 1.1.4 Random Variables and Expectations 8 1.1.5 Conditional Independence and Graphoids 11 − ## 图和概率 Graphs and Probabilities − # '''推断因果理论 A Theory of Inferred Causation''' − 1 Introduction to Probabilities, Graphs, and Causal Models 1 − − 1.1 Introduction to Probability Theory 1 第37行：
第29行： − + 第47行：
第39行： − + 第53行：
第45行： − + 第63行：
第55行： − + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + − + − 2.1 Introduction – The Basic Intuitions 42+ − 2.2 The Causal Discovery Framework 43+ − 2.3 Model Preference (Occam’s Razor) 45+ − 2.4 Stable Distributions 48+ − 2.5 Recovering DAG Structures 49+ − +
目录框架
== 书籍目录 ==
== 书籍目录 ==
'''<big>1 概率、图和因果模型介绍 Introduction to Probabilities, Graphs, and Causal Models 1</big>'''
'''1.1 概率论介绍 Introduction to Probability Theory 1'''
1.1.1 Why Probabilities? 1
1.1.1 Why Probabilities? 1
1.1.5 Conditional Independence and Graphoids 11
1.1.5 Conditional Independence and Graphoids 11
1.2 Graphs and Probabilities 12
'''1.2 图和概率 Graphs and Probabilities 12'''
1.2.1 Graphical Notation and Terminology 12
1.2.1 Graphical Notation and Terminology 12
1.2.4 Inference with Bayesian Networks 20
1.2.4 Inference with Bayesian Networks 20
1.3 Causal Bayesian Networks 21
'''1.3 Causal Bayesian Networks 21'''
1.3.1 Causal Networks as Oracles for Interventions 22
1.3.1 Causal Networks as Oracles for Interventions 22
1.3.2 Causal Relationships and Their Stability 24
1.3.2 Causal Relationships and Their Stability 24
1.4 Functional Causal Models 26
'''1.4 Functional Causal Models 26'''
1.4.1 Structural Equations 27
1.4.1 Structural Equations 27
1.4.4 Counterfactuals in Functional Models 33
1.4.4 Counterfactuals in Functional Models 33
1.5 Causal versus Statistical Terminology 38
'''1.5 Causal versus Statistical Terminology 38'''
'''<big>2 推断因果理论 A Theory of Inferred Causation 41</big>'''
'''2.1 Introduction – The Basic Intuitions 42'''
'''2.2 The Causal Discovery Framework 43'''
'''2.3 Model Preference (Occam’s Razor) 45'''
'''2.4 Stable Distributions 48'''
'''2.5 Recovering DAG Structures 49'''
'''2.6 Recovering Latent Structures 51'''
'''2.7 Local Criteria for Inferring Causal Relations 54'''
'''2.8 Nontemporal Causation and Statistical Time 57'''
'''2.9 Conclusions 59'''
2.9.1 On Minimality, Markov, and Stability 61
'''<big>3 Causal Diagrams and the Identification of Causal Effects 65</big>'''
'''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
2 A Theory of Inferred Causation 41
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
2.6 Recovering Latent Structures 51
11.9.2 Tightening the Bounds on Probabilities of Causation 398
== 各章概要 ==
== 各章概要 ==
==='''概率、图和因果模型介绍'''===
==='''概率、图和因果模型介绍'''===