A Mathematical Theory of Evidence

Name: A Mathematical Theory of Evidence
Brand: Princeton University Press
Price: 51.99 EUR
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Glenn Shafer(Autor*in)

Princeton University Press

1. Auflage

Erschienen am 30. Juni 2020

314 Seiten

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978-0-691-21469-6 (ISBN)

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Inhalt

Cover Page
Half-title Page
Title Page
Copyright Page
Dedication Page
Contents
Foreword
Preface
Chapter 1. Introduction
§1. Synopsis
§2. The Idea of Chance
§3. The Doctrine of Chances
§4. Chances as Degrees of Belief
§5. The Bayesian Theory of Partial Belief
§6. The Role of Judgment
§7. The Representation of Ignorance
§8. Combination vs. Conditioning
§9. The Representation of Probable Reasoning
§10. Statistical Inference
§11. The Bayesian Theory as a Limiting Case
§12. Probability
Chapter 2. Degrees Of Belief
§1. Subsets as Propositions
§2. Basic Probability Numbers
§3. Belief Functions
§4. Commonality Numbers
§5. Degrees of Doubt and Upper Probabilities
§6. Bayesian Belief Functions
§7. Mathematical Appendix
Chapter 3. Dempster's Rule Of Combination
§1. Combining Two Belief Functions
§2. Multiplying Commonality Numbers
§3. Combining Several Belief Functions
§4. The Weight of Conflict
§5. Conditioning Belief Functions
§6. Other Properties of Dempster's Rule
§7. Mathematical Appendix
Chapter 4. Simple And Separable Support Functions
§1. Simple Support Functions
§2. Bernoulli's Rule of Combination
§3. The Weight of Evidence
§4. Heterogeneous Evidence
§5. Conflicting Evidence
§6. Separable Support Functions
Chapter 5. The Weights Of Evidence
§1. Decomposing Separable Support Functions
§2. Combining Weights of Evidence
§3. The Assessment of Evidence
§4. The Weight of Internal Conflict
§5. The Impingement Function
§6. The Weight-of-Conflict Conjecture
§7. Some Numerical Examples
§8. Mathematical Appendix
Chapter 6. Compatible Frames Of Discernment
§1. Refinements and Coarsenings
§2. The Inner and Outer Reductions
§3. Is There an Ultimate Refinement?
§4. Families of Compatible Frames
§5. Consistent Belief Functions
§6. Independent Frames
§7. Mathematical Appendix
Chapter 7. Support Functions
§1. The Class of Support Functions
§2. Support, Dubiety, and Plausibility
§3. The Vacuous Extension of a Support Function
§4. Evidential Independence
§5. Cognitive Independence
§6. Mathematical Appendix
Chapter 8. The Discernment Of Evidence
§1. Families of Compatible Support Functions
§2. Discerning the Interaction of Evidence
§3. Discerning Weights of Evidence
§4. If the Weight-of-Conflict Conjecture is True
§5. Mathematical Appendix
Chapter 9. Quasi Support Functions
§1. Infinite Contradictory Evidence
§2. The Class of Quasi Support Functions
§3. Chances are not Degrees of Support
§4. The Bayesian Profusion of Infinite Weights
§5. Bayes' Theorem
§6. Mathematical Appendix
Chapter 10. Consonance
§1. Consonant Support Functions
§2. The Contour Function
§3. The Embarrassment of Dissonance
§4. Inferential Evidence
§5. Mathematical Appendix
Chapter 11. Statistical Evidence
§1. A Convention for Assessing Statistical Evidence
§2. The Weights of Evidence
§3. Epistemic vs. Aleatory Combination
§4. The Effect of a Bayesian Prior
§5. Discounting Statistical Evidence
§6. Specifications on Compatible Frames
§7. The Role of Supposition
§8. Perspective
§9. Mathematical Appendix
Chapter 12. The Dual Nature Of Probable Reasoning
§1. The Effect of Assumptions
§2. The Need for Assumptions
§3. Choosing our Frames of Discernment
§4. The Role of Epistemic Probability
§5. Two Tasks
Bibliography
Index

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