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.

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 'randomexperiments'

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

Review

"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."

Science

"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."

Mathematical Reviews

"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.”

SIAM News

"The 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."

Notices of the AMS

Book Description

New and original interpretation of probability theory, with applications to a wide range of subjects.