A Mathematical Theory of Evidence / / Glenn Shafer.

• Superior document: Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999
• VerfasserIn: Shafer, Glenn,
• MitwirkendeR: Dempster, A. P.,; Shafer, Glenn,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2021]; ©1976
• Year of Publication: 2021
• Language: English
• Physical Description: 1 online resource (314 p.)
• Other title: Frontmatter --; FOREWORD --; PREFACE --; CONTENTS --; CHAPTER 1. INTRODUCTION --; CHAPTER 2. DEGREES OF BELIEF --; CHAPTER 3. DEMPSTER'S RULE OF COMBINATION --; CHAPTER 4. SIMPLE AND SEPARABLE SUPPORT FUNCTIONS --; CHAPTER 5. THE WEIGHTS OF EVIDENCE --; CHAPTER 6. COMPATIBLE FRAMES OF DISCERNMENT --; CHAPTER 7. SUPPORT FUNCTIONS --; CHAPTER 8. THE DISCERNMENT OF EVIDENCE --; CHAPTER 9. QUASI SUPPORT FUNCTIONS --; CHAPTER 10. CONSONANCE --; CHAPTER 11. STATISTICAL EVIDENCE --; CHAPTER 12. THE DUAL NATURE OF PROBABLE REASONING --; BIBLIOGRAPHY --; INDEX
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9780691214696; 9783110442496
• DOI: 10.1515/9780691214696?locatt=mode:legacy
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: Glenn Shafer.

Both in science and in practical affairs we reason by combining facts only inconclusively supported by evidence. Building on an abstract understanding of this process of combination, this book constructs a new theory of epistemic probability. The theory draws on the work of A. P. Dempster but diverges from Depster's viewpoint by identifying his "lower probabilities" as epistemic probabilities and taking his rule for combining "upper and lower probabilities" as fundamental. The book opens with a critique of the well-known Bayesian theory of epistemic probability. It then proceeds to develop an alternative to the additive set functions and the rule of conditioning of the Bayesian theory: set functions that need only be what Choquet called "monotone of order of infinity." and Dempster's rule for combining such set functions. This rule, together with the idea of "weights of evidence," leads to both an extensive new theory and a better understanding of the Bayesian theory. The book concludes with a brief treatment of statistical inference and a discussion of the limitations of epistemic probability. Appendices contain mathematical proofs, which are relatively elementary and seldom depend on mathematics more advanced that the binomial theorem.