LEADER 05573nam 2200733 450 001 9910132219803321 005 20200520144314.0 010 $a1-118-76113-8 010 $a1-118-76262-2 010 $a1-118-76264-9 035 $a(CKB)3710000000096424 035 $a(EBL)1658812 035 $a(SSID)ssj0001132515 035 $a(PQKBManifestationID)11639718 035 $a(PQKBTitleCode)TC0001132515 035 $a(PQKBWorkID)11147959 035 $a(PQKB)10106181 035 $a(OCoLC)869552650 035 $a(MiAaPQ)EBC1658812 035 $a(DLC) 2014004021 035 $a(Au-PeEL)EBL1658812 035 $a(CaPaEBR)ebr10855738 035 $a(CaONFJC)MIL586311 035 $a(OCoLC)875098506 035 $a(PPN)192779362 035 $a(EXLCZ)993710000000096424 100 $a20140413h20142014 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aLower previsions /$fMatthias C.M. Troffaes, Gert de Cooman 210 1$aChichester, England :$cWiley,$d2014. 210 4$dİ2014 215 $a1 online resource (449 p.) 225 1 $aWiley Series in Probability and Statistics 300 $aDescription based upon print version of record. 311 $a0-470-72377-7 320 $aIncludes bibliographical references and index. 327 $aCover; 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 327 $a3.4 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 327 $a4.3.1 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 327 $a4.5.4 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 327 $a5.5.3 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 327 $a7.4 Lower previsions associated with proper filters 330 $a This book has two main purposes. On the one hand, it provides aconcise and systematic development of the theory of lower previsions,based on the concept of acceptability, in spirit of the work ofWilliams and Walley. On the other hand, it also extends this theory todeal with unbounded quantities, which abound in practicalapplications. Following Williams, we start out with sets of acceptable gambles. Fromthose, we derive rationality criteria---avoiding sure loss andcoherence---and inference methods---natural extension---for(unconditional) 410 0$aWiley series in probability and statistics. 606 $aProbabilities 606 $aStatistical decision 606 $aGames of chance (Mathematics) 615 0$aProbabilities. 615 0$aStatistical decision. 615 0$aGames of chance (Mathematics) 676 $a519.2 700 $aTroffaes$b Matthias C. M.$f1977-$0966960 702 $aCooman$b Gert de 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910132219803321 996 $aLower previsions$92195126 997 $aUNINA