  Probability theory : the logic of science

E.T. Jaynes ; edited by G. Larry Bretthorst

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.

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[目次]

• 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.

「Nielsen BookData」より 書名 Probability theory : the logic of science Bretthorst, G. Larry Jaynes, E. T. Jaynes E. T. Cambridge University Press 2004 Repr. with corr xxix, 727 p. 26 cm 9780521592710 BB0424151X ※クリックでCiNii Booksを表示 英語 イギリス    