【概率与统计，第1册】 Foundations of Probability Theory, Statistical Inference

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Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science
Volume I Foundations and Philosophy of Epistemic Applications of Probability Theory

Editors: William L. Harper, Clifford Alan Hooker



In May of 1973 we organized an international research colloquium on foundations of probability, statistics, and statistical theories of science at the University of Western Ontario. During the past four decades there have been striking formal advances in our understanding of logic, semantics and algebraic structure in probabilistic and statistical theories. These advances, which include the development of the relations between semantics and metamathematics, between logics and algebras and the algebraic-geometrical foundations of statistical theories (especially in the sciences), have led to striking new insights into the formal and conceptual structure of probability and statistical theory and their scientific applications in the form of scientific theory. The foundations of statistics are in a state of profound conflict. Fisher's objections to some aspects of Neyman-Pearson statistics have long been well known. More recently the emergence of Baysian statistics as a radical alternative to standard views has made the conflict especially acute. In recent years the response of many practising statisticians to the conflict has been an eclectic approach to statistical inference. Many good statisticians have developed a kind of wisdom which enables them to know which problems are most appropriately handled by each of the methods available. The search for principles which would explain why each of the methods works where it does and fails where it does offers a fruitful approach to the controversy over foundations.

Table of contents

Front Matter
Pages I-XI

Prior Probabilities and Counterfactual Conditionals
Pages 1-21

Incomplete Descriptions in the Language of Probability Theory
Pages 23-28

A Computational Complexity Viewpoint on the Stability of Relative Frequency and on Stochastic Independence
Pages 29-40

A Logic for Subjective Belief
Pages 41-72

Rational Belief Change, Popper Functions and Counterfactuals
Pages 73-115

Ramsey Test Conditionals and Iterated Belief Change (A Response to Stalnaker)
Pages 117-135

Toward an Optimization Procedure for Applying Minimum Change Principles in Probability Kinematic
Pages 137-166

Simplicity
Pages 167-203

Conditionalization, Observation, and Change of Preference
Pages 205-259

Probabilities of Conditionals
Pages 261-308

Back Matter
Pages 309-309

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Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science

Volume II Foundations and Philosophy of Statistical Inference
https://bbs.pinggu.org/thread-4979489-1-1.html

Volume III Foundations and Philosophy of Statistical Theories in the Physical Sciences
https://bbs.pinggu.org/thread-4979493-1-1.html


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Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science