Probability Theory

The standard rules of probability can be interpreted as uniquely valid principles in logic. In this book, E. T. Jaynes dispels the imaginary distinction between ‘probability theory’ and ‘statistical inference’, leaving a logical unity and simplicity, which provides greater technical power and flexibility in applications. 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 physics, mathematics, economics, chemistry and biology. It contains many exercises and problems, and is suitable for use 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. The book will be of interest to scientists working in any area where inference from incomplete information is necessary.

Spis treści:
Foreword
Preface
Part I. Principles and Elementary Applications
1. Plausible reasoning
2. The quantitative rules
3. Elementary sampling theory
4. Elementary hypothesis testing
5. Queer uses for 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, the entropy principle
12. Ignorance 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 Ap distribution and rule of succession
19. Physical measurements
20. Model comparison
21. Outliers and robustness
22. Introduction to communication theory
References
Appendix A. Other approaches to probability theory
Appendix B. Mathematical formalities and style
Appendix C. Convolutions and cumulants.