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Causation, prediction, and search. (English) Zbl 0806.62001
Lecture Notes in Statistics (Springer). 81. New York: Springer-Verlag. xxiii, 526 p. DM 86.00/ pbk (1993).
The authors investigate when and how causal influences may be reliably inferred, and their comparative strengths estimated, from statistical samples. The theory they develop is essentially axiomatic. Starting from two independent axioms on the relations between causal structure and probability distributions, they deduce the features of causal relationships and predictions that can and that cannot be reliably inferred from statistical samples. A variety of theorems concerning estimation, sampling, regression, experimental design, prediction, etc. are proved. It is found that statistical methods commonly used for causal inference are suboptimal, and that there exist asymptotically reliable, computationally efficient search procedures that conjecture causal relationships from the customes of statistical decisions made on the basis of sample data.
Chapter headings: (1) Introduction and advertisement; (2) Formal preliminaries; (3) Causation and prediction; (4) Statistical indistinguishability; (5) Discovery algorithms are causally sufficient structures; (6) Discovery algorithms without causal sufficiency; (7) Prediction; (8) Regression, causation and prediction; (9) The design of experimental studies; (10) The structure of unobserved; (11) Elaborating linear theories with unmeasured variables; (12) Open problems; (13) Proofs of theorems.
This book is intended for anyone, regardless of discipline, who is interested in the use of statistical methods to obtain scientic explanations or to predict the outcomes of actions, experiments or policies. Thus much of the book is mathematics; many of the theorems are long, difficult case arguments of a kind quite unfamiliar in statistics. The book cannot be considered as a textbook, its chapters are rich of unsolved problems and open questions.

62-02 Research exposition (monographs, survey articles) pertaining to statistics
62A01 Foundations and philosophical topics in statistics
62-07 Data analysis (statistics) (MSC2010)