{"product_id":"introduction-to-imprecise-probabilities-hardback-9780470973813","title":"Introduction to Imprecise Probabilities (Hardback) 9780470973813","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eIntroduction to Imprecise Probabilities\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eThomas Augustin (Edited by), TT Augustin (Author), Frank P. A. Coolen (Edited by), Gert de Cooman (Edited by), Matthias C. M. Troffaes (Edited by)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780470973813, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 23 May 2014\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e448 pages\u003cbr\u003e25.2 x 18 x 2.7 cm, 0.839 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eIn 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.  \u003cp\u003e\u003ci\u003eAn Introduction to Imprecise Probabilities\u003c\/i\u003e 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.\u003c\/p\u003e \u003cp\u003eEssential reading for researchers in academia, research institutes and other organizations, as well as practitioners engaged in areas such as risk analysis and engineering.\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003eIntroduction xiii\u003c\/p\u003e \u003cp\u003eA brief outline of this book xv\u003c\/p\u003e \u003cp\u003eGuide to the reader xvii\u003c\/p\u003e \u003cp\u003eContributors xxi\u003c\/p\u003e \u003cp\u003eAcknowledgements xxvii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Desirability 1\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eErik Quaeghebeur\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e1.1 Introduction 1\u003c\/p\u003e \u003cp\u003e1.2 Reasoning about and with sets of desirable gambles 2\u003c\/p\u003e \u003cp\u003e1.2.1 Rationality criteria 2\u003c\/p\u003e \u003cp\u003e1.2.2 Assessments avoiding partial or sure loss 3\u003c\/p\u003e \u003cp\u003e1.2.3 Coherent sets of desirable gambles 4\u003c\/p\u003e \u003cp\u003e1.2.4 Natural extension 5\u003c\/p\u003e \u003cp\u003e1.2.5 Desirability relative to subspaces with arbitrary vector orderings 5\u003c\/p\u003e \u003cp\u003e1.3 Deriving and combining sets of desirable gambles 6\u003c\/p\u003e \u003cp\u003e1.3.1 Gamble space transformations 6\u003c\/p\u003e \u003cp\u003e1.3.2 Derived coherent sets of desirable gambles 7\u003c\/p\u003e \u003cp\u003e1.3.3 Conditional sets of desirable gambles 8\u003c\/p\u003e \u003cp\u003e1.3.4 Marginal sets of desirable gambles 8\u003c\/p\u003e \u003cp\u003e1.3.5 Combining sets of desirable gambles 9\u003c\/p\u003e \u003cp\u003e1.4 Partial preference orders 11\u003c\/p\u003e \u003cp\u003e1.4.1 Strict preference 12\u003c\/p\u003e \u003cp\u003e1.4.2 Nonstrict preference 12\u003c\/p\u003e \u003cp\u003e1.4.3 Nonstrict preferences implied by strict ones 14\u003c\/p\u003e \u003cp\u003e1.4.4 Strict preferences implied by nonstrict ones 15\u003c\/p\u003e \u003cp\u003e1.5 Maximally committal sets of strictly desirable gambles 16\u003c\/p\u003e \u003cp\u003e1.6 Relationships with other, nonequivalent models 18\u003c\/p\u003e \u003cp\u003e1.6.1 Linear previsions 18\u003c\/p\u003e \u003cp\u003e1.6.2 Credal sets 19\u003c\/p\u003e \u003cp\u003e1.6.3 To lower and upper previsions 21\u003c\/p\u003e \u003cp\u003e1.6.4 Simplified variants of desirability 22\u003c\/p\u003e \u003cp\u003e1.6.5 From lower previsions 23\u003c\/p\u003e \u003cp\u003e1.6.6 Conditional lower previsions 25\u003c\/p\u003e \u003cp\u003e1.7 Further reading 26\u003c\/p\u003e \u003cp\u003eAcknowledgements 27\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Lower previsions 28\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eEnrique Miranda and Gert de Cooman\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction 28\u003c\/p\u003e \u003cp\u003e2.2 Coherent lower previsions 29\u003c\/p\u003e \u003cp\u003e2.2.1 Avoiding sure loss and coherence 31\u003c\/p\u003e \u003cp\u003e2.2.2 Linear previsions 35\u003c\/p\u003e \u003cp\u003e2.2.3 Sets of desirable gambles 39\u003c\/p\u003e \u003cp\u003e2.2.4 Natural extension 40\u003c\/p\u003e \u003cp\u003e2.3 Conditional lower previsions 42\u003c\/p\u003e \u003cp\u003e2.3.1 Coherence of a finite number of conditional lower previsions 45\u003c\/p\u003e \u003cp\u003e2.3.2 Natural extension of conditional lower previsions 47\u003c\/p\u003e \u003cp\u003e2.3.3 Coherence of an unconditional and a conditional lower prevision 49\u003c\/p\u003e \u003cp\u003e2.3.4 Updating with the regular extension 52\u003c\/p\u003e \u003cp\u003e2.4 Further reading 53\u003c\/p\u003e \u003cp\u003e2.4.1 The work of Williams 53\u003c\/p\u003e \u003cp\u003e2.4.2 The work of Kuznetsov 54\u003c\/p\u003e \u003cp\u003e2.4.3 The work of Weichselberger 54\u003c\/p\u003e \u003cp\u003eAcknowledgements 55\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Structural judgements 56\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eEnrique Miranda and Gert de Cooman\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 56\u003c\/p\u003e \u003cp\u003e3.2 Irrelevance and independence 57\u003c\/p\u003e \u003cp\u003e3.2.1 Epistemic irrelevance 59\u003c\/p\u003e \u003cp\u003e3.2.2 Epistemic independence 61\u003c\/p\u003e \u003cp\u003e3.2.3 Envelopes of independent precise models 63\u003c\/p\u003e \u003cp\u003e3.2.4 Strong independence 65\u003c\/p\u003e \u003cp\u003e3.2.5 The formalist approach to independence 66\u003c\/p\u003e \u003cp\u003e3.3 Invariance 67\u003c\/p\u003e \u003cp\u003e3.3.1 Weak invariance 68\u003c\/p\u003e \u003cp\u003e3.3.2 Strong invariance 69\u003c\/p\u003e \u003cp\u003e3.4 Exchangeability 71\u003c\/p\u003e \u003cp\u003e3.4.1 Representation theorem for finite sequences 72\u003c\/p\u003e \u003cp\u003e3.4.2 Exchangeable natural extension 74\u003c\/p\u003e \u003cp\u003e3.4.3 Exchangeable sequences 75\u003c\/p\u003e \u003cp\u003e3.5 Further reading 77\u003c\/p\u003e \u003cp\u003e3.5.1 Independence 77\u003c\/p\u003e \u003cp\u003e3.5.2 Invariance 77\u003c\/p\u003e \u003cp\u003e3.5.3 Exchangeability 77\u003c\/p\u003e \u003cp\u003eAcknowledgements 78\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Special cases 79\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eSébastien Destercke and Didier Dubois\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 79\u003c\/p\u003e \u003cp\u003e4.2 Capacities and \u003ci\u003en\u003c\/i\u003e-monotonicity 80\u003c\/p\u003e \u003cp\u003e4.3 2-monotone capacities 81\u003c\/p\u003e \u003cp\u003e4.4 Probability intervals on singletons 82\u003c\/p\u003e \u003cp\u003e4.5 ∞-monotone capacities 82\u003c\/p\u003e \u003cp\u003e4.5.1 Constructing ∞-monotone capacities 83\u003c\/p\u003e \u003cp\u003e4.5.2 Simple support functions 83\u003c\/p\u003e \u003cp\u003e4.5.3 Further elements 84\u003c\/p\u003e \u003cp\u003e4.6 Possibility distributions, p-boxes, clouds and related models 84\u003c\/p\u003e \u003cp\u003e4.6.1 Possibility distributions 84\u003c\/p\u003e \u003cp\u003e4.6.2 Fuzzy intervals 86\u003c\/p\u003e \u003cp\u003e4.6.3 Clouds 87\u003c\/p\u003e \u003cp\u003e4.6.4 p-boxes 88\u003c\/p\u003e \u003cp\u003e4.7 Neighbourhood models 89\u003c\/p\u003e \u003cp\u003e4.7.1 Pari-mutuel 89\u003c\/p\u003e \u003cp\u003e4.7.2 Odds-ratio 90\u003c\/p\u003e \u003cp\u003e4.7.3 Linear-vacuous 90\u003c\/p\u003e \u003cp\u003e4.7.4 Relations between neighbourhood models 91\u003c\/p\u003e \u003cp\u003e4.8 Summary 91\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Other uncertainty theories based on capacities 93\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eSébastien Destercke and Didier Dubois\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e5.1 Imprecise probability = modal logic + probability 95\u003c\/p\u003e \u003cp\u003e5.1.1 Boolean possibility theory and modal logic 95\u003c\/p\u003e \u003cp\u003e5.1.2 A unifying framework for capacity based uncertainty theories 97\u003c\/p\u003e \u003cp\u003e5.2 From imprecise probabilities to belief functions and possibility theory 97\u003c\/p\u003e \u003cp\u003e5.2.1 Random disjunctive sets 98\u003c\/p\u003e \u003cp\u003e5.2.2 Numerical possibility theory 100\u003c\/p\u003e \u003cp\u003e5.2.3 Overall picture 102\u003c\/p\u003e \u003cp\u003e5.3 Discrepancies between uncertainty theories 102\u003c\/p\u003e \u003cp\u003e5.3.1 Objectivist vs. Subjectivist standpoints 103\u003c\/p\u003e \u003cp\u003e5.3.2 Discrepancies in conditioning 104\u003c\/p\u003e \u003cp\u003e5.3.3 Discrepancies in notions of independence 107\u003c\/p\u003e \u003cp\u003e5.3.4 Discrepancies in fusion operations 109\u003c\/p\u003e \u003cp\u003e5.4 Further reading 112\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Game-theoretic probability 114\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eVladimir Vovk and Glenn Shafer\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 114\u003c\/p\u003e \u003cp\u003e6.2 A law of large numbers 115\u003c\/p\u003e \u003cp\u003e6.3 A general forecasting protocol 118\u003c\/p\u003e \u003cp\u003e6.4 The axiom of continuity 122\u003c\/p\u003e \u003cp\u003e6.5 Doob’s argument 124\u003c\/p\u003e \u003cp\u003e6.6 Limit theorems of probability 127\u003c\/p\u003e \u003cp\u003e6.7 Lévy’s zero-one law 128\u003c\/p\u003e \u003cp\u003e6.8 The axiom of continuity revisited 129\u003c\/p\u003e \u003cp\u003e6.9 Further reading 132\u003c\/p\u003e \u003cp\u003eAcknowledgements 134\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Statistical inference 135\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eThomas Augustin, Gero Walter, and Frank P. A. Coolen\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e7.1 Background and introduction 136\u003c\/p\u003e \u003cp\u003e7.1.1 What is statistical inference? 136\u003c\/p\u003e \u003cp\u003e7.1.2 (Parametric) statistical models and i.i.d. samples 137\u003c\/p\u003e \u003cp\u003e7.1.3 Basic tasks and procedures of statistical inference 139\u003c\/p\u003e \u003cp\u003e7.1.4 Some methodological distinctions 140\u003c\/p\u003e \u003cp\u003e7.1.5 Examples: Multinomial and normal distribution 141\u003c\/p\u003e \u003cp\u003e7.2 Imprecision in statistics, some general sources and motives 143\u003c\/p\u003e \u003cp\u003e7.2.1 Model and data imprecision; sensitivity analysis and ontological views on imprecision 143\u003c\/p\u003e \u003cp\u003e7.2.2 The robustness shock, sensitivity analysis 144\u003c\/p\u003e \u003cp\u003e7.2.3 Imprecision as a modelling tool to express the quality of partial knowledge 145\u003c\/p\u003e \u003cp\u003e7.2.4 The law of decreasing credibility 145\u003c\/p\u003e \u003cp\u003e7.2.5 Imprecise sampling models: Typical models and motives 146\u003c\/p\u003e \u003cp\u003e7.3 Some basic concepts of statistical models relying on imprecise probabilities 147\u003c\/p\u003e \u003cp\u003e7.3.1 Most common classes of models and notation 147\u003c\/p\u003e \u003cp\u003e7.3.2 Imprecise parametric statistical models and corresponding i.i.d. samples 148\u003c\/p\u003e \u003cp\u003e7.4 Generalized Bayesian inference 149\u003c\/p\u003e \u003cp\u003e7.4.1 Some selected results from traditional Bayesian statistics 150\u003c\/p\u003e \u003cp\u003e7.4.2 Sets of precise prior distributions, robust Bayesian inference and the generalized Bayes rule 154\u003c\/p\u003e \u003cp\u003e7.4.3 A closer exemplary look at a popular class of models: The IDM and other models based on sets of conjugate priors in exponential families 155\u003c\/p\u003e \u003cp\u003e7.4.4 Some further comments and a brief look at other models for generalized Bayesian inference 164\u003c\/p\u003e \u003cp\u003e7.5 Frequentist statistics with imprecise probabilities 165\u003c\/p\u003e \u003cp\u003e7.5.1 The nonrobustness of classical frequentist methods 166\u003c\/p\u003e \u003cp\u003e7.5.2 (Frequentist) hypothesis testing under imprecise probability: Huber-Strassen theory and extensions 169\u003c\/p\u003e \u003cp\u003e7.5.3 Towards a frequentist estimation theory under imprecise probabilities – some basic criteria and first results 171\u003c\/p\u003e \u003cp\u003e7.5.4 A brief outlook on frequentist methods 174\u003c\/p\u003e \u003cp\u003e7.6 Nonparametric predictive inference 175\u003c\/p\u003e \u003cp\u003e7.6.1 Overview 175\u003c\/p\u003e \u003cp\u003e7.6.2 Applications and challenges 177\u003c\/p\u003e \u003cp\u003e7.7 A brief sketch of some further approaches and aspects 178\u003c\/p\u003e \u003cp\u003e7.8 Data imprecision, partial identification 179\u003c\/p\u003e \u003cp\u003e7.8.1 Data imprecision 180\u003c\/p\u003e \u003cp\u003e7.8.2 Cautious data completion 181\u003c\/p\u003e \u003cp\u003e7.8.3 Partial identification and observationally equivalent models 183\u003c\/p\u003e \u003cp\u003e7.8.4 A brief outlook on some further aspects 186\u003c\/p\u003e \u003cp\u003e7.9 Some general further reading 187\u003c\/p\u003e \u003cp\u003e7.10 Some general challenges 188\u003c\/p\u003e \u003cp\u003eAcknowledgements 189\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Decision making 190\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eNathan Huntley, Robert Hable, and Matthias C. M. Troffaes\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e8.1 Non-sequential decision problems 190\u003c\/p\u003e \u003cp\u003e8.1.1 Choosing from a set of gambles 191\u003c\/p\u003e \u003cp\u003e8.1.2 Choice functions for coherent lower previsions 192\u003c\/p\u003e \u003cp\u003e8.2 Sequential decision problems 197\u003c\/p\u003e \u003cp\u003e8.2.1 Static sequential solutions: Normal form 198\u003c\/p\u003e \u003cp\u003e8.2.2 Dynamic sequential solutions: Extensive form 199\u003c\/p\u003e \u003cp\u003e8.3 Examples and applications 202\u003c\/p\u003e \u003cp\u003e8.3.1 Ellsberg’s paradox 202\u003c\/p\u003e \u003cp\u003e8.3.2 Robust Bayesian statistics 205\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Probabilistic graphical models 207\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eAlessandro Antonucci, Cassio P. de Campos, and Marco Zaffalon\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 207\u003c\/p\u003e \u003cp\u003e9.2 Credal sets 208\u003c\/p\u003e \u003cp\u003e9.2.1 Definition and relation with lower previsions 208\u003c\/p\u003e \u003cp\u003e9.2.2 Marginalization and conditioning 210\u003c\/p\u003e \u003cp\u003e9.2.3 Composition 212\u003c\/p\u003e \u003cp\u003e9.3 Independence 213\u003c\/p\u003e \u003cp\u003e9.4 Credal networks 215\u003c\/p\u003e \u003cp\u003e9.4.1 Nonseparately specified credal networks 217\u003c\/p\u003e \u003cp\u003e9.5 Computing with credal networks 220\u003c\/p\u003e \u003cp\u003e9.5.1 Credal networks updating 220\u003c\/p\u003e \u003cp\u003e9.5.2 Modelling and updating with missing data 221\u003c\/p\u003e \u003cp\u003e9.5.3 Algorithms for credal networks updating 223\u003c\/p\u003e \u003cp\u003e9.5.4 Inference on credal networks as a multilinear programming task 224\u003c\/p\u003e \u003cp\u003e9.6 Further reading 226\u003c\/p\u003e \u003cp\u003eAcknowledgements 229\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Classification 230\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eGiorgio Corani, Joaquín Abellán, Andrés Masegosa, Serafin Moral, and Marco Zaffalon\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 230\u003c\/p\u003e \u003cp\u003e10.2 Naive Bayes 231\u003c\/p\u003e \u003cp\u003e10.2.1 Derivation of naive Bayes 232\u003c\/p\u003e \u003cp\u003e10.3 Naive credal classifier (NCC) 233\u003c\/p\u003e \u003cp\u003e10.3.1 Checking Credal-dominance 233\u003c\/p\u003e \u003cp\u003e10.3.2 Particular behaviours of NCC 235\u003c\/p\u003e \u003cp\u003e10.3.3 NCC2: Conservative treatment of missing data 236\u003c\/p\u003e \u003cp\u003e10.4 Extensions and developments of the naive credal classifier 237\u003c\/p\u003e \u003cp\u003e10.4.1 Lazy naive credal classifier 237\u003c\/p\u003e \u003cp\u003e10.4.2 Credal model averaging 238\u003c\/p\u003e \u003cp\u003e10.4.3 Profile-likelihood classifiers 239\u003c\/p\u003e \u003cp\u003e10.4.4 Tree-augmented networks (TAN) 240\u003c\/p\u003e \u003cp\u003e10.5 Tree-based credal classifiers 242\u003c\/p\u003e \u003cp\u003e10.5.1 Uncertainty measures on credal sets: The maximum entropy function 242\u003c\/p\u003e \u003cp\u003e10.5.2 Obtaining conditional probability intervals with the imprecise Dirichlet model 245\u003c\/p\u003e \u003cp\u003e10.5.3 Classification procedure 246\u003c\/p\u003e \u003cp\u003e10.6 Metrics, experiments and software 249\u003c\/p\u003e \u003cp\u003e10.7 Scoring the conditional probability of the class 251\u003c\/p\u003e \u003cp\u003e10.7.1 Software 251\u003c\/p\u003e \u003cp\u003e10.7.2 Experiments 251\u003c\/p\u003e \u003cp\u003e10.7.3 Experiments comparing conditional probabilities of the class 253\u003c\/p\u003e \u003cp\u003eAcknowledgements 257\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Stochastic processes 258\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eFilip Hermans and Damjan Škulj\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e11.1 The classical characterization of stochastic processes 258\u003c\/p\u003e \u003cp\u003e11.1.1 Basic definitions 258\u003c\/p\u003e \u003cp\u003e11.1.2 Precise Markov chains 259\u003c\/p\u003e \u003cp\u003e11.2 Event-driven random processes 261\u003c\/p\u003e \u003cp\u003e11.3 Imprecise Markov chains 263\u003c\/p\u003e \u003cp\u003e11.3.1 From precise to imprecise Markov chains 264\u003c\/p\u003e \u003cp\u003e11.3.2 Imprecise Markov models under epistemic irrelevance 265\u003c\/p\u003e \u003cp\u003e11.3.3 Imprecise Markov models under strong independence 268\u003c\/p\u003e \u003cp\u003e11.3.4 When does the interpretation of independence (not) matter? 270\u003c\/p\u003e \u003cp\u003e11.4 Limit behaviour of imprecise Markov chains 272\u003c\/p\u003e \u003cp\u003e11.4.1 Metric properties of imprecise probability models 272\u003c\/p\u003e \u003cp\u003e11.4.2 The Perron-Frobenius theorem 273\u003c\/p\u003e \u003cp\u003e11.4.3 Invariant distributions 274\u003c\/p\u003e \u003cp\u003e11.4.4 Coefficients of ergodicity 275\u003c\/p\u003e \u003cp\u003e11.4.5 Coefficients of ergodicity for imprecise Markov chains 275\u003c\/p\u003e \u003cp\u003e11.5 Further reading 277\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Financial risk measurement 279\u003cbr\u003e \u003c\/b\u003e\u003ci\u003ePaolo Vicig\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e12.1 Introduction 279\u003c\/p\u003e \u003cp\u003e12.2 Imprecise previsions and betting 280\u003c\/p\u003e \u003cp\u003e12.3 Imprecise previsions and risk measurement 282\u003c\/p\u003e \u003cp\u003e12.3.1 Risk measures as imprecise previsions 283\u003c\/p\u003e \u003cp\u003e12.3.2 Coherent risk measures 284\u003c\/p\u003e \u003cp\u003e12.3.3 Convex risk measures (and previsions) 285\u003c\/p\u003e \u003cp\u003e12.4 Further reading 289\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Engineering 291\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eMichael Oberguggenberger\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e13.1 Introduction 291\u003c\/p\u003e \u003cp\u003e13.2 Probabilistic dimensioning in a simple example 295\u003c\/p\u003e \u003cp\u003e13.3 Random set modelling of the output variability 298\u003c\/p\u003e \u003cp\u003e13.4 Sensitivity analysis 300\u003c\/p\u003e \u003cp\u003e13.5 Hybrid models 301\u003c\/p\u003e \u003cp\u003e13.6 Reliability analysis and decision making in engineering 302\u003c\/p\u003e \u003cp\u003e13.7 Further reading 303\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Reliability and risk 305\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eFrank P. A. Coolen and Lev V. Utkin\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e14.1 Introduction 305\u003c\/p\u003e \u003cp\u003e14.2 Stress-strength reliability 306\u003c\/p\u003e \u003cp\u003e14.3 Statistical inference in reliability and risk 310\u003c\/p\u003e \u003cp\u003e14.4 Nonparametric predictive inference in reliability and risk 312\u003c\/p\u003e \u003cp\u003e14.5 Discussion and research challenges 317\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Elicitation 318\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eMichael Smithson\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e15.1 Methods and issues 318\u003c\/p\u003e \u003cp\u003e15.2 Evaluating imprecise probability judgements 322\u003c\/p\u003e \u003cp\u003e15.3 Factors affecting elicitation 324\u003c\/p\u003e \u003cp\u003e15.4 Matching methods with purposes 327\u003c\/p\u003e \u003cp\u003e15.5 Further reading 328\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Computation 329\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eMatthias C. M. Troffaes and Robert Hable\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e16.1 Introduction 329\u003c\/p\u003e \u003cp\u003e16.2 Natural extension 329\u003c\/p\u003e \u003cp\u003e16.2.1 Conditional lower previsions with arbitrary domains 330\u003c\/p\u003e \u003cp\u003e16.2.2 The Walley–Pelessoni–Vicig algorithm 331\u003c\/p\u003e \u003cp\u003e16.2.3 Choquet integration 332\u003c\/p\u003e \u003cp\u003e16.2.4 Möbius inverse 334\u003c\/p\u003e \u003cp\u003e16.2.5 Linear-vacuous mixture 334\u003c\/p\u003e \u003cp\u003e16.3 Decision making 335\u003c\/p\u003e \u003cp\u003e16.3.1 Γ-maximin, Γ-maximax and Hurwicz 335\u003c\/p\u003e \u003cp\u003e16.3.2 Maximality 335\u003c\/p\u003e \u003cp\u003e16.3.3 E-admissibility 336\u003c\/p\u003e \u003cp\u003e16.3.4 Interval dominance 337\u003c\/p\u003e \u003cp\u003eReferences 338\u003c\/p\u003e \u003cp\u003eAuthor index 375\u003c\/p\u003e \u003cp\u003eSubject index 385\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Wiley","offers":[{"title":"Brand New","offer_id":52278162850072,"sku":"9780470973813","price":75.79,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9780470973813.jpg?v=1781458730","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/introduction-to-imprecise-probabilities-hardback-9780470973813","provider":"Freshly Printed Books","version":"1.0","type":"link"}