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Lower previsions / / Matthias C.M. Troffaes, Gert de Cooman
| Lower previsions / / Matthias C.M. Troffaes, Gert de Cooman |
| Autore | Troffaes Matthias C. M. <1977-> |
| Pubbl/distr/stampa | Chichester, England : , : Wiley, , 2014 |
| Descrizione fisica | 1 online resource (449 p.) |
| Disciplina | 519.2 |
| Collana | Wiley Series in Probability and Statistics |
| Soggetto topico |
Probabilities
Statistical decision Games of chance (Mathematics) |
| ISBN |
1-118-76113-8
1-118-76262-2 1-118-76264-9 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Title Page; Copyright; Contents; 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 behaviour; 3.3 Bounded gambles
3.4 Sets of acceptable bounded gambles3.4.1 Rationality criteria; 3.4.2 Inference; Chapter 4 Lower previsions; 4.1 Lower and upper previsions; 4.1.1 From sets of acceptable bounded gambles to lower previsions; 4.1.2 Lower and upper previsions directly; 4.2 Consistency for lower previsions; 4.2.1 Definition and justification; 4.2.2 A more direct justification for the avoiding sure loss condition; 4.2.3 Avoiding sure loss and avoiding partial loss; 4.2.4 Illustrating the avoiding sure loss condition; 4.2.5 Consequences of avoiding sure loss; 4.3 Coherence for lower previsions 4.3.1 Definition and justification4.3.2 A more direct justification for the coherence condition; 4.3.3 Illustrating the coherence condition; 4.3.4 Linear previsions; 4.4 Properties of coherent lower previsions; 4.4.1 Interesting consequences of coherence; 4.4.2 Coherence and conjugacy; 4.4.3 Easier ways to prove coherence; 4.4.4 Coherence and monotone convergence; 4.4.5 Coherence and a seminorm; 4.5 The natural extension of a lower prevision; 4.5.1 Natural extension as least-committal extension; 4.5.2 Natural extension and equivalence; 4.5.3 Natural extension to a specific domain 4.5.4 Transitivity of natural extension4.5.5 Natural extension and avoiding sure loss; 4.5.6 Simpler ways of calculating the natural extension; 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 previsions; 5.4 Vacuous lower previsions; 5.5 {0,1}-valued lower probabilities; 5.5.1 Coherence and natural extension; 5.5.2 The link with classical propositional logic 5.5.3 The link with limits inferior5.5.4 Monotone convergence; 5.5.5 Lower oscillations and neighbourhood filters; 5.5.6 Extending a lower prevision defined on all continuous bounded gambles; Chapter 6 n-Monotone lower previsions; 6.1 n-Monotonicity; 6.2 n-Monotonicity and coherence; 6.2.1 A few observations; 6.2.2 Results for lower probabilities; 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; 7.2.1 Definition and properties; 7.2.2 Vacuous lower previsions; 7.3 Belief functions 7.4 Lower previsions associated with proper filters |
| Record Nr. | UNINA-9910132219803321 |
Troffaes Matthias C. M. <1977->
|
||
| Chichester, England : , : Wiley, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Lower previsions / / Matthias C.M. Troffaes, Gert de Cooman
| Lower previsions / / Matthias C.M. Troffaes, Gert de Cooman |
| Autore | Troffaes Matthias C. M. <1977-> |
| Pubbl/distr/stampa | Chichester, England : , : Wiley, , 2014 |
| Descrizione fisica | 1 online resource (449 p.) |
| Disciplina | 519.2 |
| Collana | Wiley Series in Probability and Statistics |
| Soggetto topico |
Probabilities
Statistical decision Games of chance (Mathematics) |
| ISBN |
1-118-76113-8
1-118-76262-2 1-118-76264-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Title Page; Copyright; Contents; 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 behaviour; 3.3 Bounded gambles
3.4 Sets of acceptable bounded gambles3.4.1 Rationality criteria; 3.4.2 Inference; Chapter 4 Lower previsions; 4.1 Lower and upper previsions; 4.1.1 From sets of acceptable bounded gambles to lower previsions; 4.1.2 Lower and upper previsions directly; 4.2 Consistency for lower previsions; 4.2.1 Definition and justification; 4.2.2 A more direct justification for the avoiding sure loss condition; 4.2.3 Avoiding sure loss and avoiding partial loss; 4.2.4 Illustrating the avoiding sure loss condition; 4.2.5 Consequences of avoiding sure loss; 4.3 Coherence for lower previsions 4.3.1 Definition and justification4.3.2 A more direct justification for the coherence condition; 4.3.3 Illustrating the coherence condition; 4.3.4 Linear previsions; 4.4 Properties of coherent lower previsions; 4.4.1 Interesting consequences of coherence; 4.4.2 Coherence and conjugacy; 4.4.3 Easier ways to prove coherence; 4.4.4 Coherence and monotone convergence; 4.4.5 Coherence and a seminorm; 4.5 The natural extension of a lower prevision; 4.5.1 Natural extension as least-committal extension; 4.5.2 Natural extension and equivalence; 4.5.3 Natural extension to a specific domain 4.5.4 Transitivity of natural extension4.5.5 Natural extension and avoiding sure loss; 4.5.6 Simpler ways of calculating the natural extension; 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 previsions; 5.4 Vacuous lower previsions; 5.5 {0,1}-valued lower probabilities; 5.5.1 Coherence and natural extension; 5.5.2 The link with classical propositional logic 5.5.3 The link with limits inferior5.5.4 Monotone convergence; 5.5.5 Lower oscillations and neighbourhood filters; 5.5.6 Extending a lower prevision defined on all continuous bounded gambles; Chapter 6 n-Monotone lower previsions; 6.1 n-Monotonicity; 6.2 n-Monotonicity and coherence; 6.2.1 A few observations; 6.2.2 Results for lower probabilities; 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; 7.2.1 Definition and properties; 7.2.2 Vacuous lower previsions; 7.3 Belief functions 7.4 Lower previsions associated with proper filters |
| Record Nr. | UNINA-9910824361803321 |
|
Troffaes Matthias C. M. <1977->
|
||
| Chichester, England : , : Wiley, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||