Causation, Prediction, and Search

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Springer Science & Business Media, Dec 6, 2012 - Mathematics - 530 pages
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

Formal Preliminaries
25
Axioms and Explications
41
Statistical Indistinguishability
87
Discovery Algorithms for Causally Sufficient Structures
103
Discovery Algorithms without Causal Sufficiency
163
Prediction
201
Regression Causation and Prediction
238
The Design of Empirical Studies
259
The Structure of the Unobserved
306
Elaborating Linear Theories with Unmeasured Variables
323
Open Problems
354
Proofs of Theorems
367
Glossary
481
Bibliography
495
Index
517
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