A comprehensive introduction to the role of probability theory in general scientific endeavour. This book provides an original interpretation of probability theory, showing the subject to be an extension of logic, and presenting new results and applications. Ideal for scientists working in any area involving inference from incomplete information.
A comprehensive introduction to the role of probability theory in general scientific endeavour. This book provides an original interpretation of probability theory, showing the subject to be an extension of logic, and presenting new results and applications. Ideal for scientists working in any area involving inference from incomplete information.
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.
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.
Rezensionen
'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
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