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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.
Contents
1. Introduction and Advertisement.- 1.1 The Issue.- 1.2 Advertisements.- 1.3 Themes.- 2. Formal Preliminaries.- 2.1 Graphs.- 2.2 Probability.- 2.3 Graphs and Probability Distributions.- 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.- 3.3 Causality and Probability.- 3.4 The Axioms.- 3.5 Discussion of the Conditions.- 3.6 Bayesian Interpretations.- 3.7 Consequences of The Axioms.- 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.- 5.3 The Wermuth-Lauritzen Algorithm.- 5.4 New Algorithms.- 5.5 Statistical Decisions.- 5.6 Reliability and Probabilities of Error.- 5.7 Estimation.- 5.8 Examples and Applications.- 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.- 8.3 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.- 9.5 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.- 10.4 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.- 11.3 The LISREL and EQS Procedures.- 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.- 12.2 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.
