- 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

- 2.1 Introduction
- 2.2 The Causal Modeling 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 Causal Relations
- 2.8 Non-Temporal Causation and Statistical Time
- 2.9 Conclusions
- 2.9.1 On Minimality, Markov, and Stability

- 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
- 3.2.4 Identification in 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 Robin's
*G*-estimation

- 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 Plans
- 4.4.1 Motivation
- 4.4.2 Plan Identification: Notation and Assumptions
- 4.4.3 Plan Identification: A General Criterion
- 4.4.4 Plan Identification: A Procedure
- 4.5 Direct Effects and Their Identification
- 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 Average Direct Effects

- 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
- 5.2.2 Testing the Testable
- 5.2.3 Model Equivalence
- 5.3 Graphs and Identifiability
- 5.3.1 Parameter Identification in Linear Models
- 5.3.2 Comparison to Nonparametric Identification
- 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?
- 5.4.2 Interpretation of Effect Decomposition
- 5.4.3 Exogeneity, Superexogeneity and Other Frills
- 5.5 Conclusion

- 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 Enchangeability
- 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
- 6.2.2 Causal and Associational Definitions
- 6.3 How the Associational Criterion Fails
- 6.3.1 Failing Sufficiency via Marginality
- 6.3.2 Failing Sufficiency Due Closed-World Assumptions
- 6.3.3 Failing Necessity via Barren Proxies
- 6.3.4 Failing Necessity via Incidental Cancelations
- 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
- 6.5.3 Exchangeability versus Structural Analysis of Confounding
- 6.6 Conclusions
- Acknowledgment

- 7.1 Structural Model Semantics
- 7.1.1 Definitions: Causal Models, Actions, and Counterfactuals
- 7.1.2 Evaluating Counterfactuals: Deterministic Analysis
- 7.1.3 Evaluating Counterfactuals: Probabilistic Analysis
- 7.1.4 The Twin-Networks 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
- 7.2.3 Causal Explanations, Utterances, and Their Interpretation
- 7.2.4 From Mechanisms to Actions to Causation
- 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
- 7.4 Structural and Similarity-based Counterfactuals
- 7.4.1 Relations to Lewis's Counterfactuals
- 7.4.2 Axiomatic Comparison
- 7.4.3 Imaging versus Conditioning
- 7.4.4 Relation to Neyman-Rubin Framework
- 7.4.5 Exogeneity Revisited: Counterfactuals and Graphs
- 7.5 Structural versus Probabilistic Causality
- 7.5.1 The Reliance on Temporal Ordering
- 7.5.2 The Perils of Circularity
- 7.5.3 The Closed-World Assumption
- 7.5.4 Singular versus General Causes
- 7.5.5 Summary

- 8.1 Introduction
- 8.1.1 Imperfect and Indirect Experiments
- 8.1.2 Noncompliance and Intent to Treat
- 8.2 Bounding Causal Effects
- 8.2.1 Problem Formulation
- 8.2.2 The Evolution of Potential-Response Rariables
- 8.2.3 Linear Programming Formulation
- 8.2.4 The Natural Bounds
- 8.2.5 Effect of Treatment on the Treated
- 8.2.6 Example: The Effect of Cholestyramine
- 8.3 Counterfactuals and Legal Responsibility}
- 8.4 A Test for Instruments
- 8.5 Causal Inference From Finite Sample
- 8.5.1 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

- 9.1 Introduction
- 9.2 Necessary and Sufficient Causes: Conditions of Identification
- 9.2.1 Definitions, Notation, and Basic Relationships
- 9.2.2 Bounds and Basic Relationships under Exogeneity
- 9.2.3 Identifiability under Monotonicity and Exogeneity
- 9.2.4 Identifiability under Monotonicity and NonExogeneity
- 9.3 Examples and Applications
- 9.3.1 Example-1: Betting against a Fair Coin
- 9.3.2 Example-2: The Firing Squad
- 9.3.3 Example-3: The Effect of Radiation on Leukemia
- 9.3.4 Example-4: Legal Responsibility from Experimental and NonExperimental Data
- 9.3.5 Summary of Results
- 9.4 Identification in Non-monotonic Models
- 9.5 Conclusions

- 10.1 Introduction: The Insufficiency of Necessary Causation
- 10.1.1 Singular causes revisited
- 10.1.2 Preemption and the Role of Structural Information
- 10.1.3 Overdetermination and Quasi-Dependence
- 10.1.4 Mackie's INUS Condition
- 10.2 Production, Dependence, and Sustenance
- 10.3 Causal Beams and Sustenance-Based Causation
- 10.3.1 Causal beams: Definitions and Implications
- 10.3.2 Examples: From Disjunction to General Formulas
- 10.3.3 Beams, Preemption, and the Probability of Single-Event Causation
- 10.3.4 Path-Switching Causation
- 10.3.5 Temporal Preemption
- 10.4 Conclusions

- A public lecture delivered November 1996 as part of the UCLA Faculty Research Lectureship Program