# zbMATH — the first resource for mathematics

Probability theory. The logic of science. Edited and with a foreword by G. Larry Bretthorst. (English) Zbl 1045.62001
Cambridge: Cambridge University Press (ISBN 0-521-59271-2/hbk). xxix, 727 p. (2003).
The book concerns basic concepts of probability theory and statistics. Theory is built through principles of logic. The book contains a large number of various applications and comments, including discussions on paradoxes of probability theory. From the author’s summary:
This book goes beyond the conventional mathematics of probability theory, viewing the subject in a wider context. New results are discussed, along with applications of probability theory to a wide variety of problems in physiscs, mathematics, economics, chemistry and biology. It contains many exercices and problems, and is suitable for use a as a textbook on graduate level courses involving data analysis. The material is aimed at readers who are already familiar with applied mathematics at an advanced undergraduate level or higher.
Chapter headings: Part I: Principles and elementary applications. (1) Plausible reasoning; (2) The quantitative rules; (3) Elementary sampling theory; (4) Elementary hypothesis testing; (5) Queer uses of probability theory; (6) Elementary parameter estimation; (7) The central, Gaussian or normal distribution; (8) Sufficiency, ancillarity, and all that; (9) Repetitive experiments: probability and frequency; (10) Physics of random experiments.
Part II: Advanced applications. (11) discrete prior probabilities: entropy principle; (12) Ingnorance priors and transformation groups; (13) Decision theory, historical background; (14) Simple applications of decision theory; (15) Paradoxes of probability theory; (16) Orthodox methods: historical background; (17) Principles and pathology of orthodox statistics; (18) The $$A_p$$ distribution and rule of succession; (19) Phycical measurements; (20) Model comparisons; (21) Outliers and robustness; (22) Introduction to communication theory. Appendix A: Other approaches; Appendix B: Mathematical formalities and style; Appendix C: Convolutions and cumulants.
The book could be of interest to scientists working in areas where inference of incomplete information should be made.

##### MSC:
 62-02 Research exposition (monographs, survey articles) pertaining to statistics 62A01 Foundations and philosophical topics in statistics 60-02 Research exposition (monographs, survey articles) pertaining to probability theory 60A05 Axioms; other general questions in probability
Full Text: