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9780470723777 - Matthias C. M. Troffaes: Lower Previsions
1
Matthias C. M. Troffaes (?):

Lower Previsions (?)

ISBN: 9780470723777 (?) bzw. 0470723777, in Englisch, Wiley, gebundenes Buch, neu

102,48 ($ 109,00)¹(versandkostenfrei, unverbindlich)
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Von Händler/Antiquariat
Lower-Previsions~~Matthias-C-M-Troffaes, Lower Previsions, Hardcover
Kommentar des Händlers/Antiquariats:
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Bestellnummer des Händlers: 9780470723777
Bestellnummer bei der Plattform BarnesAndNoble.com: bn-9780470723777
Kategorie: Science>Statistics & Probability>Statistics & Probability
Daten vom 11.02.2017 09:14h
ISBN (andere Schreibweisen): 0-470-72377-7, 978-0-470-72377-7
9780470723777 - Matthias C. M. Troffaes, Gert de Cooman: Lower Previsions
2
Matthias C. M. Troffaes, Gert de Cooman (?):

Lower Previsions (?)

ISBN: 9780470723777 (?) bzw. 0470723777, in Englisch, Wiley, neu

94,12 (C$ 131,00)¹(unverbindlich)
In Stock, plus shipping
Von Händler/Antiquariat
Matthias C. M. Troffaes, Gert de Cooman, Books, Science and Nature, Lower Previsions, This book has two main purposes. On the one hand, it provides aconcise and systematic development of the theory of lower previsions,based on the concept of acceptability, in spirit of the work ofWilliams and Walley. On the other hand, it also extends this theory todeal with unbounded quantities, which abound in practicalapplications.Following Williams, we start out with sets of acceptable gambles. Fromthose, we derive rationality criteria---avoiding sure loss andcoherence---and inference methods---natural extension---for(unconditional) lower previsions. We then proceed to study variousaspects of the resulting theory, including the concept of expectation(linear previsions), limits, vacuous models, classical propositionallogic, lower oscillations, and monotone convergence. We discussn-monotonicity for lower previsions, and relate lower previsions withChoquet integration, belief functions, random sets, possibilitymeasures, various integrals, symmetry, and representation theoremsbased on the Bishop-De Leeuw theorem.Next, we extend the framework of sets of acceptable gambles to consideralso unbounded quantities. As before, we again derive rationalitycriteria and inference methods for lower previsions, this time alsoallowing for conditioning. We apply this theory to constructextensions of lower previsions from bounded random quantities to alarger set of random quantities, based on ideas borrowed from thetheory of Dunford integration.A first step is to extend a lower prevision to random quantities thatare bounded on the complement of a null set (essentially boundedrandom quantities). This extension is achieved by a natural extensionprocedure that can be motivated by a rationality axiom stating thatadding null random quantities does not affect acceptability.In a further step, we approximate unbounded random quantities by asequences of bounded ones, and, in essence, we identify those forwhich the induced lower prevision limit does not depend on the detailsof the approximation. We call those random quantities 'previsible'. Westudy previsibility by cut sequences, and arrive at a simplesufficient condition. For the 2-monotone case, we establish a Choquetintegral representation for the extension. For the general case, weprove that the extension can always be written as an envelope ofDunford integrals. We end with some examples of the theory.
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Bestellnummer des Händlers: 978047072377
Bestellnummer bei der Plattform Indigo.ca: id-978047072377
Kategorie: Books>Science and Nature
Daten vom 11.02.2017 09:14h
ISBN (andere Schreibweisen): 0-470-72377-7, 978-0-470-72377-7
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9780470723777 - Troffaes, Matthias C. M.; Cooman, Gert de: Lower Previsions
3
Troffaes, Matthias C. M.; Cooman, Gert de (?):

Lower Previsions (?)

ISBN: 9780470723777 (?) bzw. 0470723777, in Englisch, Wiley, neu, E-Book

88,82 ($ 94,47)¹(versandkostenfrei, unverbindlich)
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Mathematics, This book has two main purposes. On the one hand, it provides a concise and systematic development of the theory of lower previsions, based on the concept of acceptability, in spirit of the work of Williams and Walley. On the other hand, it also extends this theory to deal with unbounded quantities, which abound in practical applications. Following Williams, we start out with sets of acceptable gambles. From those, we derive rationality criteria---avoiding sure loss and coherence---and inference methods---natural extension---for (unconditional) lower previsions. We then proceed to study various aspects of the resulting theory, including the concept of expectation (linear previsions), limits, vacuous models, classical propositional logic, lower oscillations, and monotone convergence. We discuss n-monotonicity for lower previsions, and relate lower previsions with Choquet integration, belief functions, random sets, possibility measures, various integrals, symmetry, and representation theorems based on the Bishop-De Leeuw theorem. Next, we extend the framework of sets of acceptable gambles to consider also unbounded quantities. As before, we again derive rationality criteria and inference methods for lower previsions, this time also allowing for conditioning. We apply this theory to construct extensions of lower previsions from bounded random quantities to a larger set of random quantities, based on ideas borrowed from the theory of Dunford integration. A first step is to extend a lower prevision to random quantities that are bounded on the complement of a null set (essentially bounded random quantities). This extension is achieved by a natural extension procedure that can be motivated by a rationality axiom stating that adding null random quantities does not affect acceptability. In a further step, we approximate unbounded random quantities by a sequences of bounded ones, and, in essence, we identify those for which the induced lower prevision limit does not depend on the details of the approximation. We call those random quantities 'previsible'. We study previsibility by cut sequences, and arrive at a simple sufficient condition. For the 2-monotone case, we establish a Choquet integral representation for the extension. For the general case, we prove that the extension can always be written as an envelope of Dunford integrals. We end with some examples of the theory. eBook
Bestellnummer des Händlers: 1658812
Bestellnummer bei der Plattform eBooks.com: eb-1658812
Kategorie: Mathematics
Daten vom 11.02.2017 09:14h
ISBN (andere Schreibweisen): 0-470-72377-7, 978-0-470-72377-7
9780470723777 - Lower Previsions
4

Lower Previsions (?)

ISBN: 9780470723777 (?) bzw. 0470723777, in Englisch, Wiley, United States of America, neu

78,16 (£ 66,62)¹(versandkostenfrei, unverbindlich)
in-stock
Von Händler/Antiquariat
This book has two main purposes. On the one hand, it provides aconcise and systematic development of the theory of lower previsions, based on the concept of acceptability, in spirit of the work ofWilliams and Walley. On the other hand, it also extends this theory todeal with unbounded quantities, which abound in practicalapplications. Following Williams, we start out with sets of acceptable gambles. Fromthose, we derive rationality criteria-avoiding sure loss andcoherence-and inference methods-natural extension-for(unconditional) lower previsions. We then proceed to study variousaspects of the resulting theory, including the concept of expectation(linear previsions), limits, vacuous models, classical propositionallogic, lower oscillations, and monotone convergence. We discussn-monotonicity for lower previsions, and relate lower previsions withChoquet integration, belief functions, random sets, possibilitymeasures, various integrals, symmetry, and representation theoremsbased on the Bishop-De Leeuw theorem. Next, we extend the framework of sets of acceptable gambles to consideralso unbounded quantities. As before, we again derive rationalitycriteria and inference methods for lower previsions, this time alsoallowing for conditioning. We apply this theory to constructextensions of lower previsions from bounded random quantities to alarger set of random quantities, based on ideas borrowed from thetheory of Dunford integration. A first step is to extend a lower prevision to random quantities thatare bounded on the complement of a set (essentially boundedrandom quantities). This extension is achieved by a natural extensionprocedure that can be motivated by a rationality axiom stating thatadding random quantities does not affect acceptability.
Bestellnummer des Händlers: 9780470723777
Bestellnummer bei der Plattform Wordery.com: 9780470723777
Daten vom 11.02.2017 09:14h
ISBN (andere Schreibweisen): 0-470-72377-7, 978-0-470-72377-7
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53 Auflage. Stand 1. März 1998. 789 Seiten. OKart. Gut erhalten.
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