Lecture Notes in Statistics

1. Introduction and Advertisement.- 1.1 The Issue.- 1.2 Advertisements.- 1.2.1 Bayes Networks from the Data.- 1.2.2 Structural Equation Models from the Data.- 1.2.3 Selection of Regressors.- 1.2.4 Causal Inference without Experiment.- 1.2.5 The Structure of the Unobserved.- 1.3 Themes.- 2. Formal Preliminaries.- 2.1 Graphs.- 2.2 Probability.- 2.3 Graphs and Probability Distributions.- 2.3.1 Directed Acyclic Graphs.- 2.3.2 Directed Independence Graphs.- 2.3.3 Faithfulness.- 2.3.4 d-separation.- 2.3.5 Linear Structures.- 2.4 Undirected Independence Graphs.- 2.5 Deterministic and Pseudo-Indeterministic Systems.- 2.6 Background Notes.- 3. Causation and Prediction: Axioms and Explications.- 3.1 Conditionals.- 3.2 Causation.- 3.2.1 Direct vs. Indirect Causation.- 3.2.2 Events and Variables.- 3.2.3 Examples.- 3.2.4 Representing Causal Relations with Directed Graphs.- 3.3 Causality and Probability.- 3.3.1 Deterministic Causal Structures.- 3.3.2 Pseudo-Indeterministic and Indeterministic Causal Structures.- 3.4 The Axioms.- 3.4.1 The Causal Markov Condition.- 3.4.2 The Causal Minimality Condition.- 3.4.3 The Faithfulness Condition.- 3.5 Discussion of the Conditions.- 3.5.1 The Causal Markov and Minimality Conditions.- 3.5.2 Faithfulness and Simpson's Paradox.- 3.6 Bayesian Interpretations.- 3.7 Consequences of The Axioms.- 3.7.1 d-Separation.- 3.7.2 The Manipulation Theorem.- 3.8 Determinism.- 3.9 Background Notes.- 4. Statistical Indistinguishability.- 4.1 Strong Statistical Indistinguishability.- 4.2 Faithful Indistinguishability.- 4.3 Weak Statistical Indistinguishability.- 4.4 Rigid Indistinguishability.- 4.5 The Linear Case.- 4.6 Redefining Variables.- 4.7 Background Notes.- 5. Discovery Algorithms for Causally Sufficient Structures.- 5.1 Discovery Problems.- 5.2 Search Strategies in Statistics.- 5.2.1 The Wrong Hypothesis Space.- 5.2.2 Computational and Statistical Limitations.- 5.2.3 Generating a Single Hypothesis.- 5.2.4 Other Approaches.- 5.2.5 Bayesian Methods.- 5.3 The Wermuth-Lauritzen Algorithm.- 5.4 New Algorithms.- 5.4.1 The SGS Algorithm.- 5.4.2 The PC Algorithm.- 5.4.3 The IG (Independence Graph) Algorithm.- 5.4.4 Variable Selection.- 5.4.5 Incorporating Background Knowledge.- 5.5 Statistical Decisions.- 5.6 Reliability and Probabilities of Error.- 5.7 Estimation.- 5.8 Examples and Applications.- 5.8.1 The Causes of Publishing Productivity.- 5.8.2 Education and Fertility.- 5.8.3 The Female Orgasm.- 5.8.4 The American Occupational Structure.- 5.8.5 The ALARM Network.- 5.8.6 Virginity.- 5.8.7 The Leading Crowd.- 5.8.8 Influences on College Plans.- 5.8.9 Abortion Opinions.- 5.8.10 Simulation Tests with Random Graphs.- 5.9 Conclusion.- 5.10 Background Notes.- 6. Discovery Algorithms without Causal Sufficiency.- 6.1 Introduction.- 6.2 The PC Algorithm and Latent Variables.- 6.3 Mistakes.- 6.4 Inducing Paths.- 6.5 Inducing Path Graphs.- 6.6 Partially Oriented Inducing Path Graphs.- 6.7 Algorithms for Causal Inference with Latent Common Causes.- 6.8 Theorems on Detectable Causal Influence.- 6.9 Non-Independence Constraints.- 6.10 Generalized Statistical Indistinguishability and Linearity.- 6.11 The Tetrad Representation Theorem.- 6.12 An Example: Math Marks and Causal Interpretation.- 6.13 Background Notes.- 7. Prediction.- 7.1 Introduction.- 7.2 Prediction Problems.- 7.3 Rubin-Holland-Pratt-Schlaifer Theory.- 7.4 Prediction with Causal Sufficiency.- 7.5 Prediction without Causal Sufficiency.- 7.6 Examples.- 7.7 Conclusion.- 7.8 Background Notes.- 8. Regression, Causation and Prediction.- 8.1 When Regression Fails to Measure Influence.- 8.2 A Solution and Its Application.- 8.2.1 Components of the Armed Forces Qualification Test.- 8.2.2 The Causes of Spartina Biomass.- 8.2.3 The Effects of Foreign Investment on Political Repression.- 8.2.4 More Simulation Studies.- 8.3 Error Probabilities for Specification Searches.- 8.4 Conclusion.- 9. The Design of Empirical Studies.- 9.1 Observational or Experimental Study?.- 9.2 Selecting Variables.- 9.3 Sampling.- 9.4 Ethical Issues in Experimental Design.- 9.4.1 The Kadane/Sedransk/Seidenfeld Design.- 9.4.2 Causal Reasoning in the Experimental Design.- 9.4.3 Towards Ethical Trials.- 9.5 An Example: Smoking and Lung Cancer.- 9.6 Appendix.- 10. The Structure of the Unobserved.- 10.1 Introduction.- 10.2 An Outline of the Algorithm.- 10.3 Finding Almost Pure Measurement Models.- 10.3.1 Intra-Construct Foursomes.- 10.3.2 Cross-Construct Foursomes.- 10.4 Facts about the Unobserved Determined by the Observed.- 10.5 Unifying the Pieces.- 10.6 Simulation Tests.- 10.7 Conclusion.- 11. Elaborating Linear Theories with Unmeasured Variables.- 11.1 Introduction.- 11.2 The Procedure.- 11.2.1 Scoring.- 11.2.2 Search.- 11.3 The LISREL and EQS Procedures.- 11.3.1 Input and Output.- 11.3.2 Scoring.- 11.3.3 The LISREL VI Search.- 11.3.4 The EQS Search.- 11.4 The Primary Study.- 11.4.1 The Design of Comparative Simulation Studies.- 11.4.2 Study Design.- 11.5 Results.- 11.6 Reliability and Informativeness.- 11.7 Using LISREL and EQS as Adjuncts to Search.- 11.8 Limitations of the TETRAD II Elaboration Search.- 11.9 Some Morals for Statistical Search.- 12. Open Problems.- 12.1 Feedback, Reciprocal Causation, and Cyclic Graphs.- 12.1.1 Mason's Theorem.- 12.1.2 Time Series and Cyclic Graphs.- 12.1.3 The Markov Condition, Factorizability and Faithfulness.- 12.1.4 Discovery Procedures.- 12.2 Indistinguishability Relations.- 12.3 Time series and Granger Causality.- 12.4 Model Specification and Parameter Estimation from the Same Data Base.- 12.5 Conditional Independence Tests.- 13. Proofs of Theorems.- 13.1 Theorem 2.1.- 13.2 Theorem 3.1.- 13.3 Theorem 3.2.- 13.4 Theorem 3.3.- 13.5 Theorem 3.4.- 13.6 Theorem 3.5.- 13.7 Theorem 3.6 (Manipulation Theorem).- 13.8 Theorem 3.7.- 13.9 Theorem 4.1.- 13.10 Theorem 4.2.- 13.11 Theorem 4.3.- 13.12 Theorem 4.4.- 13.13 Theorem 4.5.- 13.14 Theorem 4.6.- 13.15 Theorem 5.1.- 13.16 Theorem 6.1.- 13.17 Theorem 6.2..- 13.18 Theorem 6.3.- 13.19 Theorem 6.4.- 13.20 Theorem 6.5.- 13.21 Theorem 6.6.- 13.22 Theorem 6.7.- 13.23 Theorem 6.8.- 13.24 Theorem 6.9.- 13.25 Theorem 6.10 (Tetrad Representation Theorem).- 13.26 Theorem 6.11.- 13.27 Theorem 7.1.- 13.28 Theorem 7.2.- 13.29 Theorem 7.3.- 13.30 Theorem 7.4.- 13.31 Theorem 7.5.- 13.32 Theorem 9.1.- 13.33 Theorem 9.2.- 13.34 Theorem 10.1.- 13.35 Theorem 10.2.- 13.36 Theorem 11.1.