Cover -- CAUSALITY: Models, Reasoning, and Inference Second Edition -- Series Page -- Title -- Copyright -- Dedication -- Contents -- Preface to the First Edition -- Preface to the Second Edition -- CHAPTER ONE Introduction to Probabilities, Graphs, and Causal Models -- 1.1 INTRODUCTION TO PROBABILITY THEORY -- 1.1.1 Why Probabilities? -- 1.1.2 Basic Concepts in Probability Theory -- 1.1.3 Combining Predictive and Diagnostic Supports -- 1.1.4 Random Variables and Expectations -- 1.1.5 Conditional Independence and Graphoids -- 1.2 GRAPHS AND PROBABILITIES -- 1.2.1 Graphical Notation and Terminology -- 1.2.2 Bayesian Networks -- 1.2.3 The d-Separation Criterion -- 1.2.4 Inference with Bayesian Networks -- 1.3 CAUSAL BAYESIAN NETWORKS -- 1.3.1 Causal Networks as Oracles for Interventions -- 1.3.2 Causal Relationships and Their Stability -- 1.4 FUNCTIONAL CAUSAL MODELS -- 1.4.1 Structural Equations -- 1.4.2 Probabilistic Predictions in Causal Models -- 1.4.3 Interventions and Causal Effects in Functional Models -- 1.4.4 Counterfactuals in Functional Models -- 1.5 CAUSAL VERSUS STATISTICAL TERMINOLOGY -- Causal versus Statistical Concepts -- Two Mental Barriers to Causal Analysis -- CHAPTER TWO A Theory of Inferred Causation -- Preface -- 2.1 INTRODUCTION - THE BASIC INTUITIONS -- 2.2 THE CAUSAL DISCOVERY FRAMEWORK -- 2.3 MODEL PREFERENCE (OCCAM'S RAZOR) -- 2.4 STABLE DISTRIBUTIONS -- 2.5 RECOVERING DAG STRUCTURES -- 2.6 RECOVERING LATENT STRUCTURES -- 2.7 LOCAL CRITERIA FOR INFERRING CAUSAL RELATIONS -- 2.8 NONTEMPORAL CAUSATION AND STATISTICAL TIME -- 2.9 CONCLUSIONS -- 2.9.1 On Minimality, Markov, and Stability -- Relation to the Bayesian Approach -- Postscript for the Second Edition -- CHAPTER THREE Causal Diagrams and the Identification of Causal Effects -- Preface -- 3.1 INTRODUCTION -- 3.2 INTERVENTION IN MARKOVIAN MODELS.

3.2.1 Graphs as Models of Interventions -- 3.2.2 Interventions as Variables -- 3.2.3 Computing the Effect of Interventions -- An Example: Dynamic Process Control -- Summary -- 3.2.4 Identification of Causal Quantities -- 3.3 CONTROLLING CONFOUNDING BIAS -- 3.3.1 The Back-Door Criterion -- 3.3.2 The Front-Door Criterion -- 3.3.3 Example: Smoking and the Genotype Theory -- 3.4 A CALCULUS OF INTERVENTION -- 3.4.1 Preliminary Notation -- 3.4.2 Inference Rules -- 3.4.3 Symbolic Derivation of Causal Effects: An Example -- 3.4.4 Causal Inference by Surrogate Experiments -- 3.5 GRAPHICAL TESTS OF IDENTIFIABILITY -- 3.5.1 Identifying Models -- 3.5.2 Nonidentifying Models -- 3.6 DISCUSSION -- 3.6.1 Qualifications and Extensions -- 3.6.2 Diagrams as a Mathematical Language -- 3.6.3 Translation from Graphs to Potential Outcomes -- 3.6.4 Relations to Robins's G-Estimation -- Personal Remarks and Acknowledgments -- Postscript for the Second Edition -- Complete identification results -- Applications and Critics -- Chapter Road Map to the Main Results -- CHAPTER FOUR Actions, Plans, and Direct Effects -- Preface -- 4.1 INTRODUCTION -- 4.1.1 Actions, Acts, and Probabilities -- 4.1.2 Actions in Decision Analysis -- 4.1.3 Actions and Counterfactuals -- 4.2 CONDITIONAL ACTIONS AND STOCHASTIC POLICIES -- 4.3 WHEN IS THE EFFECT OF AN ACTION IDENTIFIABLE? -- 4.3.1 Graphical Conditions for Identification -- 4.3.2 Remarks on Efficiency -- 4.3.3 Deriving a Closed-Form Expression for Control Queries -- 4.3.4 Summary -- 4.4 THE IDENTIFICATION OF DYNAMIC PLANS -- 4.4.1 Motivation -- 4.4.2 Plan Identification: Notation and Assumptions -- 4.4.3 Plan Identification: The Sequential Back-Door Criterion -- 4.4.4 Plan Identification: A Procedure -- 4.5 DIRECT AND INDIRECT EFFECTS -- 4.5.1 Direct versus Total Effects -- 4.5.2 Direct Effects, Definition, and Identification.

4.5.3 Example: Sex Discrimination in College Admission -- 4.5.4 Natural Direct Effects -- 4.5.5 Indirect Effects and the Mediation Formula -- CHAPTER FIVE Causality and Structural Models in Social Science and Economics -- Preface -- 5.1 INTRODUCTION -- 5.1.1 Causality in Search of a Language -- 5.1.2 SEM: How Its Meaning Became Obscured -- 5.1.3 Graphs as a Mathematical Language -- 5.2 GRAPHS AND MODEL TESTING -- 5.2.1 The Testable Implications of Structural Models -- Preliminary Notation -- d-Separation and Partial Correlations -- 5.2.2 Testing the Testable -- 5.2.3 Model Equivalence -- Generating Equivalent Models -- The Significance of Equivalent Models -- 5.3 GRAPHS AND IDENTIFIABILITY -- 5.3.1 Parameter Identification in Linear Models -- 5.3.2 Comparison to Nonparametric Identification -- Parametric versus Nonparametric Models: An Example -- 5.3.3 Causal Effects: The Interventional Interpretation of Structural Equation Models -- 5.4 SOME CONCEPTUAL UNDERPINNINGS -- 5.4.1 What Do Structural Parameters Really Mean? -- Structural Equations: Operational Definition -- The Structural Parameters: Operational Definition -- The Mystical Error Term: Operational Definition -- The Mystical Error Term: Conceptual Interpretation -- 5.4.2 Interpretation of Effect Decomposition -- 5.4.3 Exogeneity, Superexogeneity, and Other Frills -- The Mystical Error Term Revisited -- 5.5 CONCLUSION -- 5.6 Postscript for the Second Edition -- 5.6.1 An Econometric Awakening? -- 5.6.2 Identification in Linear Models -- 5.6.3 Robustness of Causal Claims -- Acknowledgments -- CHAPTER SIX Simpson's Paradox, Confounding, and Collapsibility -- Preface -- 6.1 SIMPSON'S PARADOX: AN ANATOMY -- 6.1.1 A Tale of a Non-Paradox -- 6.1.2 A Tale of Statistical Agony -- 6.1.3 Causality versus Exchangeability -- 6.1.4 A Paradox Resolved (Or: What Kind of Machine Is Man?).

6.2 WHY THERE IS NO STATISTICAL TEST FOR CONFOUNDING, WHY MANY THINK THERE IS, AND WHY THEY ARE ALMOST RIGHT 6.2.1 Introduction -- 6.2.1 Introduction -- Associational Criterion -- 6.2.2 Causal and Associational Definitions -- 6.3 HOW THE ASSOCIATIONAL CRITERION FAILS -- 6.3.1 Failing Sufficiency via Marginality -- 6.3.2 Failing Sufficiency via Closed-World Assumptions -- 6.3.3 Failing Necessity via Barren Proxies -- 6.3.4 Failing Necessity via Incidental Cancellations -- 6.4 STABLE VERSUS INCIDENTAL UNBIASEDNESS -- 6.4.1 Motivation -- 6.4.2 Formal Definitions -- 6.4.3 Operational Test for Stable No-Confounding -- 6.5 CONFOUNDING, COLLAPSIBILITY, AND EXCHANGEABILITY -- 6.5.1 Confounding and Collapsibility -- 6.5.2 Confounding versus Confounders -- Proof of Necessity -- 6.5.3 Exchangeability versus Structural Analysis of Confounding -- 6.6 CONCLUSIONS -- Acknowledgments -- Postscript for the Second Edition -- CHAPTER SEVEN The Logic of Structure-Based Counterfactuals -- Preface -- 7.1 STRUCTURAL MODEL SEMANTICS -- 7.1.1 Definitions: Causal Models, Actions, and Counterfactuals -- 7.1.2 Evaluating Counterfactuals: Deterministic Analysis -- Evaluating Standard Sentences -- Evaluating Action Sentences -- Evaluating Counterfactuals -- 7.1.3 Evaluating Counterfactuals: Probabilistic Analysis -- 7.1.4 The Twin Network Method -- 7.2 APPLICATIONS AND INTERPRETATION OF STRUCTURAL MODELS -- 7.2.1 Policy Analysis in Linear Econometric Models: An Example -- 7.2.2 The Empirical Content of Counterfactuals -- Counterfactuals with Intrinsic Nondeterminism -- 7.2.3 Causal Explanations, Utterances, and Their Interpretation -- 7.2.4 From Mechanisms to Actions to Causation -- Action, Mechanisms, and Surgeries -- Laws versus Facts -- Mechanisms and Causal Relationships -- 7.2.5 Simon's Causal Ordering -- 7.3 AXIOMATIC CHARACTERIZATION.

7.3.1 The Axioms of Structural Counterfactuals -- 7.3.2 Causal Effects from Counterfactual Logic: An Example -- 7.3.3 Axioms of Causal Relevance -- Remark on the Transitivity of Causal Dependence -- Proof -- 7.4 STRUCTURAL AND SIMILARITY-BASED COUNTERFACTUALS -- 7.4.1 Relations to Lewis's Counterfactuals -- Causality from Counterfactuals -- Structure versus Similarity -- 7.4.2 Axiomatic Comparison -- 7.4.3 Imaging versus Conditioning -- 7.4.4 Relations to the Neyman-Rubin Framework -- A Language in Search of a Model -- Graphical versus Counterfactual Analysis -- 7.4.5 Exogeneity and Instruments: Counterfactual and Graphical Definitions -- Instrumental Variables: Three Definitions -- 7.5 STRUCTURAL VERSUS PROBABILISTIC CAUSALITY -- 7.5.1 The Reliance on Temporal Ordering -- 7.5.2 The Perils of Circularity -- 7.5.3 Challenging the Closed-World Assumption, with Children -- 7.5.4 Singular versus General Causes -- 7.5.5 Summary -- Acknowledgments -- CHAPTER EIGHT Imperfect Experiments: Bounding Effects and Counterfactuals -- Preface -- 8.1 INTRODUCTION -- 8.1.1 Imperfect and Indirect Experiments -- 8.1.2 Noncompliance and Intent to Treat -- 8.2 BOUNDING CAUSAL EFFECTS WITH INSTRUMENTAL VARIABLES -- 8.2.1 Problem Formulation: Constrained Optimization -- 8.2.2 Canonical Partitions: The Evolution of Finite-Response Variables -- 8.2.3 Linear Programming Formulation -- 8.2.4 The Natural Bounds -- 8.2.5 Effect of Treatment on the Treated (ETT) -- 8.2.6 Example: The Effect of Cholestyramine -- 8.3 COUNTERFACTUALS AND LEGAL RESPONSIBILITY -- 8.4 A TEST FOR INSTRUMENTS -- The Instrumental Inequality -- 8.5 A BAYESIAN APPROACH TO NONCOMPLIANCE -- 8.5.1 Bayesian Methods and Gibbs Sampling -- 8.5.2 The Effects of Sample Size and Prior Distribution -- 8.5.3 Causal Effects from Clinical Data with Imperfect Compliance -- 8.5.4 Bayesian Estimate of Single-Event Causation.

8.6 CONCLUSION.