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.
Author(s): E. T. Jaynes
Year: 2003
Language: English
Pages: 758
Contents......Page 8
Preface......Page 20
Part 1 Principles and elementary applications......Page 31
1 Plausible reasoning......Page 33
2 The quantitative rules......Page 54
3 Elementary sampling theory......Page 81
4 Elementary hypothesis testing......Page 116
5 Queer uses for probability theory......Page 149
6 Elementary parameter estimation......Page 179
7 The central, Gaussian or normal distribution......Page 228
8 Sufficiency, ancillarity, and all that......Page 273
9 Repetitive experiments: probability and frequency......Page 300
10 Physics of ‘randomexperiments’......Page 344
Part II Advanced applications......Page 12
11 Discrete prior probabilities: the entropy principle......Page 373
12 Ignorance priors and transformation groups......Page 402
13 Decision theory, historical background......Page 427
14 Simple applications of decision theory......Page 456
15 Paradoxes of probability theory......Page 481
16 Orthodox methods: historical background......Page 520
17 Principles and pathology of orthodox statistics......Page 539
18 The Ap distribution and rule of succession......Page 583
19 Physical measurements......Page 619
20 Model comparison......Page 631
21 Outliers and robustness......Page 645
22 Introduction to communication theory......Page 657
AppendixA Other approaches to probability theory......Page 681
AppendixB Mathematical formalities and style......Page 691
AppendixC Convolutions and cumulants......Page 707
References......Page 713
Subject index......Page 754
