PROBABILITY THEORY -- The logic of science

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 by  E. T. Jaynes

Dedicated to the Memory of Sir Harold Jeffreys, who saw the truth and preserved it.

Fragmentary Edition of June 1994

Short Contents

• PREFACE

PART A - PRINCIPLES AND ELEMENTARY APPLICATIONS

• Chapter 1 Plausible Reasoning
• Chapter 2 Quantitative Rules: The Cox Theorems
• Fig. 2-1
• Chapter 3 Elementary Sampling Theory
• Chapter 4 Elementary Hypothesis Testing
• Fig. 4-1
• Chapter 5 Queer Uses for Probability Theory
• Chapter 6 Elementary Parameter Estimation
• Fig. 6-1
• Fig. 6-2
• Chapter 7 The Central Gaussian, or Normal, Distribution
• Chapter 8 Sufficiency, Ancillarity, and All That
• Chapter 9 Repetitive Experiments: Probability and Frequency
• Chapter 10 Physics of ``Random Experiments’‘
• Chapter 11 The Entropy Principle
• Chapter 12 Ignorance Priors — Transformation Groups
• Chapter 13 Decision Theory: Historical Survey
• Chapter 14 Simple Applications of Decision Theory
• Chapter 15 Paradoxes of Probability Theory
• Fig. 15-1
• Chapter 16 Orthodox Statistics: Historical Background
• Chapter 17 Principles and Pathology of Orthodox Statistics
• Chapter 18 The A —Distribution and Rule of Succession

PART B — ADVANCED APPLICATIONS

• Chapter 19 Physical Measurements
• Chapter 20 Regression and Linear Models
• Chapter 21 Estimation with Cauchy and t—Distributions
• Chapter 22 Time Series Analysis and Autoregressive Models
• Chapter 23 Spectrum / Shape Analysis
• Chapter 24 Model Comparison and Robustness
• Chapter 25 Image Reconstruction
• Chapter 26 Marginalization Theory
• Chapter 27 Communication Theory
• Chapter 28 Optimal Antenna and Filter Design
• Chapter 29 Statistical Mechanics
• Chapter 30 Maximum Entropy: Matrix Formulation

APPENDICES

• Appendix A Other Approaches to Probability Theory
• Appendix B Formalities and Mathematical Style
• Appendix C Convolutions and Cumulants
• Appendix D Dirichlet Integrals and Generating Functions
• Appendix E The Binomial — Gaussian Hierarchy of Distributions
• Appendix F Fourier Analysis
• Appendix G Infinite Series
• Appendix H Matrix Analysis and Computation
• Appendix I Computer Programs

REFERENCES

• List of references