An Introduction to Imprecise Probabilities
(Sprache: Englisch)
In recent years, the theory has become widely accepted and has been further developed, but a detailed introduction is needed in order to make the material available and accessible to a wide audience. This will be the first book providing such an...
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Klappentext zu „An Introduction to Imprecise Probabilities “
In recent years, the theory has become widely accepted and has been further developed, but a detailed introduction is needed in order to make the material available and accessible to a wide audience. This will be the first book providing such an introduction, covering core theory and recent developments which can be applied to many application areas. All authors of individual chapters are leading researchers on the specific topics, assuring high quality and up-to-date contents.An Introduction to Imprecise Probabilities provides a comprehensive introduction to imprecise probabilities, including theory and applications reflecting the current state if the art. Each chapter is written by experts on the respective topics, including: Sets of desirable gambles; Coherent lower (conditional) previsions; Special cases and links to literature; Decision making; Graphical models; Classification; Reliability and risk assessment; Statistical inference; Structural judgments; Aspects of implementation (including elicitation and computation); Models in finance; Game-theoretic probability; Stochastic processes (including Markov chains); Engineering applications.
Essential reading for researchers in academia, research institutes and other organizations, as well as practitioners engaged in areas such as risk analysis and engineering.
Inhaltsverzeichnis zu „An Introduction to Imprecise Probabilities “
PrefaceIntroduction
Acknowledgements
Outline of this Book and Guide to Readers
Contributors
1 Desirability
1.1 Introduction
1.2 Reasoning about and with Sets of Desirable Gambles
1.2.1 Rationality Criteria
1.2.2 Assessments Avoiding Partial or Sure Loss
1.2.3 Coherent Sets of Desirable Gambles
1.2.4 Natural Extension
1.2.5 Desirability Relative to Subspaces with Arbitrary Vector Orderings
1.3 Deriving & Combining Sets of Desirable Gambles
1.3.1 Gamble Space Transformations
1.3.2 Derived Coherent Sets of Desirable Gambles
1.3.3 Conditional Sets of Desirable Gambles
1.3.4 Marginal Sets of Desirable Gambles
1.3.5 Combining Sets of Desirable Gambles
1.4 Partial Preference Orders
1.4.1 Strict Preference
1.4.2 Nonstrict Preference
1.4.3 Nonstrict Preferences Implied by Strict Ones
1.4.4 Strict Preferences Implied by Nonstrict Ones
1.5 Maximally Committal Sets of Strictly Desirable Gambles
1.6 Relationships with Other, Nonequivalent Models
1.6.1 Linear Previsions
1.6.2 Credal Sets
1.6.3 To Lower and Upper Previsions
1.6.4 Simplified Variants of Desirability
1.6.5 From Lower Previsions
1.6.6 Conditional Lower Previsions
1.7 Further Reading
2 Lower Previsions
2.1 Introduction
2.2 Coherent Lower Previsions
2.2.1 Avoiding Sure Loss and Coherence
2.2.2 Linear Previsions
2.2.3 Sets of Desirable Gambles
2.2.4 Natural Extension
2.3 Conditional Lower Previsions
2.3.1 Coherence of a Finite Number of Conditional Lower Previsions
2.3.2 Natural Extension of Conditional Lower Previsions
2.3.3 Coherence of an Unconditional and a Conditional Lower Prevision
2.3.4 Updating with the Regular
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Extension
2.4 Further Reading
2.4.1 The Work of Williams
2.4.2 The Work of Kuznetsov
2.4.3 The Work of Weichselberger
3 Structural Judgements
3.1 Introduction
3.2 Irrelevance and Independence
3.2.1 Epistemic Irrelevance
3.2.2 Epistemic Independence
3.2.3 Envelopes of Independent Precise Models
3.2.4 Strong Independence
3.2.5 The Formalist Approach to Independence
3.3 Invariance
3.3.1 Weak Invariance
3.3.2 Strong Invariance
3.4 Exchangeability.
3.4.1 Representation Theorem for Finite Sequences
3.4.2 Exchangeable Natural Extension
3.4.3 Exchangeable Sequences
3.5 Further Reading
3.5.1 Independence.
3.5.2 Invariance
3.5.3 Exchangeability
4 Special Cases
4.1 Introduction
4.2 Capacities and n-monotonicity
4.3 2-monotone Capacities
4.4 Probability Intervals on Singletons
4.5 1-monotone Capacities
4.5.1 Constructing 1-monotone Capacities
4.5.2 Simple Support Functions
4.5.3 Further Elements
4.6 Possibility Distributions, p-boxes, Clouds and Related Models.
4.6.1 Possibility Distributions
4.6.2 Fuzzy Intervals
4.6.3 Clouds
4.6.4 p-boxes.
4.7 Neighbourhood Models
4.7.1 Pari-mutuel
4.7.2 Odds-ratio
4.7.3 Linear-vacuous
4.7.4 Relations between Neighbourhood Models
4.8 Summary
5 Other Uncertainty Theories Based on Capacities
5.1 Imprecise Pr
2.4 Further Reading
2.4.1 The Work of Williams
2.4.2 The Work of Kuznetsov
2.4.3 The Work of Weichselberger
3 Structural Judgements
3.1 Introduction
3.2 Irrelevance and Independence
3.2.1 Epistemic Irrelevance
3.2.2 Epistemic Independence
3.2.3 Envelopes of Independent Precise Models
3.2.4 Strong Independence
3.2.5 The Formalist Approach to Independence
3.3 Invariance
3.3.1 Weak Invariance
3.3.2 Strong Invariance
3.4 Exchangeability.
3.4.1 Representation Theorem for Finite Sequences
3.4.2 Exchangeable Natural Extension
3.4.3 Exchangeable Sequences
3.5 Further Reading
3.5.1 Independence.
3.5.2 Invariance
3.5.3 Exchangeability
4 Special Cases
4.1 Introduction
4.2 Capacities and n-monotonicity
4.3 2-monotone Capacities
4.4 Probability Intervals on Singletons
4.5 1-monotone Capacities
4.5.1 Constructing 1-monotone Capacities
4.5.2 Simple Support Functions
4.5.3 Further Elements
4.6 Possibility Distributions, p-boxes, Clouds and Related Models.
4.6.1 Possibility Distributions
4.6.2 Fuzzy Intervals
4.6.3 Clouds
4.6.4 p-boxes.
4.7 Neighbourhood Models
4.7.1 Pari-mutuel
4.7.2 Odds-ratio
4.7.3 Linear-vacuous
4.7.4 Relations between Neighbourhood Models
4.8 Summary
5 Other Uncertainty Theories Based on Capacities
5.1 Imprecise Pr
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Bibliographische Angaben
- Autoren: Frank Coolen , Matthias Troffaes , Gert de Cooman
- 2014, 1. Auflage, 448 Seiten, Maße: 17,6 x 25,1 cm, Gebunden, Englisch
- Herausgegeben: Thomas Augustin, Frank P. A. Coolen, Gert de Cooman, Matthias C. M. Troffaes
- Verlag: Wiley & Sons
- ISBN-10: 0470973811
- ISBN-13: 9780470973813
- Erscheinungsdatum: 09.06.2014
Sprache:
Englisch
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