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.

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)

##### MSC:

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 |