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Author Troffaes, Matthias C. M., 1977-

Title Lower previsions / Matthias C.M. Troffaes. Gert de Cooman
Published Chichester, West Sussex, United Kingdom : Wiley, 2014
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Description 1 online resource
Series Wiley series in probability and statistics
Wiley series in probability and statistics.
Contents Wiley Series in Probability and Statistics; Title Page; Copyright; Dedication; Preface; Acknowledgements; Chapter 1: Preliminary notions and definitions; 1.1 Sets of numbers; 1.2 Gambles; 1.3 Subsets and their indicators; 1.4 Collections of events; 1.5 Directed sets and Moore-Smith limits; 1.6 Uniform convergence of bounded gambles; 1.7 Set functions, charges and measures; 1.8 Measurability and simple gambles; 1.9 Real functionals; 1.10 A useful lemma; Part I: Lower Previsions on Bounded Gambles; Chapter 2: Introduction; Chapter 3: Sets of acceptable bounded gambles; 3.1 Random variables
3.2 Belief and behaviour3.3 Bounded gambles; 3.4 Sets of acceptable bounded gambles; Chapter 4: Lower previsions; 4.1 Lower and upper previsions; 4.2 Consistency for lower previsions; 4.3 Coherence for lower previsions; 4.4 Properties of coherent lower previsions; 4.5 The natural extension of a lower prevision; 4.6 Alternative characterisations for avoiding sure loss, coherence, and natural extension; 4.7 Topological considerations; Chapter 5: Special coherent lower previsions; 5.1 Linear previsions on finite spaces; 5.2 Coherent lower previsions on finite spaces
5.3 Limits as linear previsions5.4 Vacuous lower previsions; 5.5 {0,1}-valued lower probabilities; Chapter 6: n-Monotone lower previsions; 6.1 n-Monotonicity; 6.2 n-Monotonicity and coherence; 6.3 Representation results; Chapter 7: Special n-monotone coherent lower previsions; 7.1 Lower and upper mass functions; 7.2 Minimum preserving lower previsions; 7.3 Belief functions; 7.4 Lower previsions associated with proper filters; 7.5 Induced lower previsions; 7.6 Special cases of induced lower previsions; 7.7 Assessments on chains of sets; 7.8 Possibility and necessity measures
7.9 Distribution functions and probability boxesChapter 8: Linear previsions, integration and duality; 8.1 Linear extension and integration; 8.2 Integration of probability charges; 8.3 Inner and outer set function, completion and other extensions; 8.4 Linear previsions and probability charges; 8.5 The S-integral; 8.6 The Lebesgue integral; 8.7 The Dunford integral; Chapter 9: Examples of linear extension; 9.1 Distribution functions; 9.2 Limits inferior; 9.3 Lower and upper oscillations; 9.4 Linear extension of a probability measure
9.5 Extending a linear prevision from continuous bounded gambles9.6 Induced lower previsions and random sets; Chapter 10: Lower previsions and symmetry; 10.1 Invariance for lower previsions; 10.2 An important special case; 10.3 Interesting examples; Chapter 11: Extreme lower previsions; 11.1 Preliminary results concerning real functionals; 11.2 Inequality preserving functionals; 11.3 Properties of inequality preserving functionals; 11.4 Infinite non-negative linear combinations of inequality preserving functionals; 11.5 Representation results
Bibliography Includes bibliographical references and index
Notes Print version record and CIP data provided by publisher
Subject Games of chance (Mathematics)
Statistical decision.
Form Electronic book
Author Cooman, Gert de.
LC no. 2014004021
ISBN 0470723777
1118761138 (ePub)
1118762649 (Adobe PDF)
9781118761137 (ePub)
9781118762646 (Adobe PDF)