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Going beyond the conventional mathematics of probability theory, this study views the subject in a wider context. It discusses new results, along with applications of probability theory to a variety of problems. The book contains many exercises and is suitable for use as a textbook on graduate-level courses involving data analysis. Aimed at readers already familiar with applied mathematics at an advanced undergraduate level or higher, it is of interest to scientists concerned with inference from incomplete information.Read more
- Unique interpretation of probability theory, containing new and original work by the author
- Applications of probability theory to a wide range of problems in physics and other areas
- The interpretation of probability as an extension of logic, dispelling many of the paradoxes usually associated with probability theory
Reviews & endorsements
"...tantalizing ideas...one of the most useful and least familiar applications of Bayesian theory...Probability Theory [is] considerably more entertaining reading than the average statistics textbook...the conceptual points that underlie his attacks are often right on."
ScienceSee more reviews
"This is a work written by a scientist for scientists. As such it is to be welcomed. The reader will certainly find things with which he disagrees, but he will also find much that will cause him to think deeply not only on his usual practice by also on statistics and probability in general. Probability Theory: the Logic of Science is, for both statisticians and scientists, more than just 'recommended reading': it should be prescribed."
"...the rewards of reading Probability Theory can be immense."
Physics Today, Ralph Baierlein
This is not an ordinary text. It is an unabashed, hard sell of the Bayesian approach to statistics. It is wonderfully down to earth, with hundreds of telling examples. Everyone who is interested in the problems or applications of statistics should have a serious look.
"[T]he author thinks for himself…and writes in a lively way about all sorts of things. It is worth dipping into it if only for vivid expressions of opinion...There are many books on Bayesian statistics, but few with this much color."
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- Date Published: June 2003
- format: Hardback
- isbn: 9780521592710
- length: 753 pages
- dimensions: 256 x 180 x 39 mm
- weight: 1.68kg
- availability: Temporarily unavailable - available from April 2017
Table of Contents
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
Appendix A. Other approaches to probability theory
Appendix B. Mathematical formalities and style
Appendix C. Convolutions and cumulants.
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