Causation, Prediction, and Search

This book is intended for anyone, regardless of discipline, who is interested in the use of statistical methods to help obtain scientific explanations or to predict the outcomes of actions, experiments or policies. Much of G. Udny Yule's work illustrates a vision of statistics whose goal is to investigate when and how causal influences may be reliably inferred, and their comparative strengths estimated, from statistical samples. Yule's enterprise has been largely replaced by Ronald Fisher's conception, in which there is a fundamental cleavage between experimental and non­ experimental inquiry, and statistics is largely unable to aid in causal inference without randomized experimental trials. Every now and then members of the statistical community express misgivings about this turn of events, and, in our view, rightly so. Our work represents a return to something like Yule's conception of the enterprise of theoretical statistics and its potential practical benefits. If intellectual history in the 20th century had gone otherwise, there might have been a discipline to which our work belongs. As it happens, there is not. We develop material that belongs to statistics, to computer science, and to philosophy; the combination may not be entirely satisfactory for specialists in any of these subjects. We hope it is nonetheless satisfactory for its purpose.

Contenu

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.