{"product_id":"introduction-to-imprecise-probabilities-9780470973813","title":"Introduction to Imprecise Probabilities","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e* The first book to chart the development and applications of this growing subject.      * Provides a comprehensive introduction to imprecise probabilities, including theory and applications reflecting the current state of the art.      * Each chapter is written by leading experts in their field.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\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","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402470826327,"sku":"9780470973813","price":72.86,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780470973813.jpg?v=1730480501","url":"https:\/\/bookcurl.com\/products\/introduction-to-imprecise-probabilities-9780470973813","provider":"Book Curl","version":"1.0","type":"link"}