Probabilistic Analysis of Belief Functions: IFSR International Series in Systems Science and Systems Engineering, cartea 16
Autor Ivan Kramosilen Limba Engleză Paperback – 21 sep 2012
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Specificații
ISBN-13: 9781461351450
ISBN-10: 1461351456
Pagini: 236
Ilustrații: XVII, 214 p.
Dimensiuni: 155 x 235 x 12 mm
Greutate: 0.34 kg
Ediția:2001
Editura: Springer Us
Colecția Springer
Seria IFSR International Series in Systems Science and Systems Engineering
Locul publicării:New York, NY, United States
ISBN-10: 1461351456
Pagini: 236
Ilustrații: XVII, 214 p.
Dimensiuni: 155 x 235 x 12 mm
Greutate: 0.34 kg
Ediția:2001
Editura: Springer Us
Colecția Springer
Seria IFSR International Series in Systems Science and Systems Engineering
Locul publicării:New York, NY, United States
Public țintă
ResearchCuprins
1 Introduction.- 1.1 Uncertainty in the World Around.- 1.2 Classical Probability Theory - Uncertainty as Randomness.- 1.3 Dempster-Shafer Approach to Uncertainty Processing.- 1.4 Relations to the Theory of General Systems.- 2 Preliminaries on Axiomatic Probability Theory.- 2.1 Probability Spaces and Random Variables.- 2.2 Some Intuition and Motivation Behind.- 2.3 Conditional Probabilities and Stochastic Independence.- 2.4 The Most Simple Setting of the Strong Law of Large Numbers.- 3 Probabilistic Model of Decision Making under Uncertainty.- 3.1 An Intuitive Background to Decision Making Theory.- 3.2 Decision Making under Uncertainty.- 3.3 Statistical Decision Functions.- 3.4 The Bayesian and the Minimax Principles.- 3.5 An Example and Some Problems Involved.- 4 Basic Elements of Dempster-Shafer Theory.- 4.1 From Intuition to Compatibility Relations.- 4.2 From Compatibility Relations to Belief Functions.- 4.3 Some Remarks and Comments.- 4.4 Semantical Consistence and Correctness of Belief Functions.- 5 Elementary Properties of Belief Functions.- 5.1 Plausibility Functions.- 5.2 Basic Probability Assignments and Belief Functions.- 5.3 Super-Additivity of Belief Functions.- 5.4 Some Particular Cases of Belief Functions.- 5.5 Belief Functions and the Case of Total Ignorance.- 6 Probabilistic Analysis of Dempster Combination Rule.- 6.1 Knowledge Acquisition as Dynamical Process.- 6.2 Combining Compatibility Relations.- 6.3 Towards Dempster Combination Rule.- 6.4 Elementary Properties of Dempster Combination Rule.- 6.5 Dual Combination Rule.- 7 Nonspecificity Degrees of Basic Probability Assignments.- 7.1 The Most Simple Case of Nonspecificity Degrees.- 7.2 Nonspecificity Degrees of Dempster Products.- 7.3 Quasi-Deconditioning.- 7.4 The Case of Dual Combination Rule.- 8 Belief Functions Induced by Partial Compatibility Relations.- 8.1 Compatibility Relations over Sets of States and Sets of Empirical Values.- 8.2 Partial Generalized Compatibility Relations.- 8.3 Belief Functions Defined by Partial Generalized Compatibility Relations.- 8.4 Partial Generalized Compatibility Relations with the Same Compatibility Relation.- 8.5 Approximations of Belief Functions by the Partial Generalized Ones.- 9 Belief Functions over Infinite State Spaces.- 9.1 Towards Infinite Basic Spaces.- 9.2 Definability of Degrees of Belief for Subsets of Infinite Spaces.- 9.3 Extensions of Degrees of Belief to Non-Regular Subsets.- 9.4 Elementary Properties of Extended Belief Functions.- 9.5 Bounds of Application of Extended Belief Functions.- 9.6 Survey of Approximations of Degrees of Belief over Infinite Spaces.- 10 Boolean Combinations of Set-Valued Random Variables.- 10.1 Combining Set-Valued Random Variables.- 10.2 Belief Functions Defined by Unions of Set-Valued Random Variables.- 10.3 Belief Functions Defined by Intersections of Set-Valued Random Variables.- 11 Belief Functions with Signed and Nonstandard Values.- 11.1 The Inversion Problem for Degrees of Belief and Belief Functions.- 11.2 Signed Measures.- 11.3 Degrees of Belief Are Leaving the Unit Interval of Reals.- 11.4 Dempster Combination Rule for Basic Signed Measure Assignments.- 11.5 Inversion Rule for Basic Signed Measure Assignments.- 11.6 Almost Invertibility of Basic Signed Measure Assignments.- 11.7 Degrees of Belief with Nonstandard Values.- 11.8 An Abstract Algebraic Approach to the Inversion Problem.- 12 Jordan Decomposition of Signed Belief Functions.- 12.1 Hahn Decomposition Theorem for Signed Measures.- 12.2 Jordan Decomposition of Signed Belief Functions.- 12.3 Generalizing Conditioned Belief Functions.- 13 Monte-Carlo Estimations for Belief Functions.- 13.1 Strong Law of Large Numbers Applied to Belief Functions.- 13.2 Towards Monte-Carlo Algorithms for Belief Functions.- 13.3 Asymptotic Properties of Monte-Carlo Estimations of Belief Functions.- 13.4 Chebyshev Inequality for Monte-Carlo Estimations of Belief Functions.- 14 Boolean-Valued and Boolean-Like Processed Belief Functions.- 14.1 Intuition, Motivation and Preliminaries on Boolean Algebras.- 14.2 Boolean-Valued Probability Measures.- 14.3 Boolean-Valued Belief and Plausibility Functions.- 14.4 Boolean-Like Structure over The Unit Interval of Real Numbers.- 14.5 Probability Measures with Values in Boolean-Like Structured Unit Interval of Real Numbers.- 14.6 Basic Nonstandard Probability Assignments.- 15 References.- 16 Index.