广义概率论发展前景——关于趣味数学与置信函数实际应用的一些原创观点(英文)

Preface CHAPTER 1. Introduction Part 1. Belief calculus CHAPTER 2. Shafer's mathematical theory of evidence 1. Belief functions 2. Dempster's rule of combination 3. Simple and separable support functions 4. Families of compatible frames of discernment 5. Support functions 6. Impact of the evidence 7. Quasi support functions 8. Consonant belief functions CHAPTER 3. State of the art 1. The alternative interpretations of belief functions 2. Frameworks and approaches 3. Conditional belief functions 4. Statistical inference and estimation 5. Decision making 6. Efficient implementation of belief calculus 7. Continuous belief functions 8. Other theoretical developments 9. Relation with other mathematical theories of uncertainty 10. Applications Part 2. Advances CHAPTER 4. A geometric approach to belief calculus 1. The space of belief functions 2. Simplicial form of the belief space 3. The bundle structure of the belief space 4. Global geometry of Dempster's rule 5. Pointwise geometry of Dempster's rule 6. Applications of the geometric approach 7. Conclusive comments CHAPTER 5. Algebraic structure of the families of compatible frames 1. Axiom analysis 2. Monoidal structure of families of frames 3. Lattice structure of families of frames 4. Semimodular structure of families of frames CHAPTER 6. Algebra of independence and conflict I. Independence of frames and Dempster's combination 2. An algebraic study of independence of flames 3. Independence on lattices versus independence of frames 4. Perspectives 5. Conclusive comments Part 3. Visions CHAPTER 7. Data association and the total belief theorem 1. The data association problem 2. The total belief theorem 3. The restricted total belief theorem 4. Conclusive comments CHAPTER 8. Belief Modeling Regression 1. Scenario 2. Learning evidential models 3. Regression 4. Assessing evidential models 5. Results on human pose estimation 6. Discussion 7. Towards evidential tracking 8. Conclusive comments Part 4. Conclusions CHAPTER 9. Conclusions Bibliography 编辑手记