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Statistical reasoning with imprecise probabilities. (English) Zbl 0732.62004
Monographs on Statistics and Applied Probability, 42. London etc.: Chapman and Hall. xii, 706 p. £58.00 (1991).
This book is about methods of reasoning and statistical inferences using imprecise probabilities. The methods are based on a behavioral interpretation of probability and principles of coherence. The purpose of this book is (i) to develop a mathematical theory of imprecise probabilities with applications to statistical inference and decision, based on a behavioral interpretation and principles of coherence, (ii) to compare it with the Bayesian theory, (iii) to consider the ways in which a behavioral theory differs from Bayesian sensitivity analysis, and (iv) to suggest some useful models for assessing imprecise probabilities.
The material of the book is covered in 9 chapters besides an Appendix. The fundamental ideas of imprecise probabilities, coherence and assessment strategies are given in the introductory chapter. Chapters 2 to 5 are concerned with unconditional probability. Chapters 6 to 9 deal with conditional probability and statistical models. The basic mathematical theory of coherence is presented in Chapter 2 (for unconditional probability), Chapter 6 (for conditional probability) and Chapter 7 (for statistical models). The mathematical theory is presented at a simple level, making use of methods and results from linear functional analysis.
Reviewer: K.Alam (Clemson)

62-02 Research exposition (monographs, survey articles) pertaining to statistics
62A01 Foundations and philosophical topics in statistics
62C10 Bayesian problems; characterization of Bayes procedures
62C99 Statistical decision theory