A mathematical theory of evidence / Glenn Shafer.

Format:

Book

Author/Creator:

Shafer, Glenn, 1946- author.

Contributor:

Dempster, A. P., Contributor.

Shafer, Glenn, Contributor.

Language:

English

Subjects (All):

Probabilities.

Mathematical statistics.

Evidence.

Physical Description:

1 online resource (xiii, 297 pages)

Place of Publication:

Princeton, New Jersey ; London : Princeton University Press, [1976]

Summary:

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.

Contents:

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

Notes:

Description based on print version record.

Includes bibliographical references pages 287-291 and index.

ISBN:

9780691214696

0691214697

OCLC:

1248759935