| Description |
1 online resource (xxvi, 404 pages) |
| Summary |
"In 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. An Introduction to Imprecise Probabilities 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. Essential reading for researchers in academia, research institutes and other organizations, as well as practitioners engaged in areas such as risk analysis and engineering"-- Provided by publisher |
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"Provides a comprehensive introduction to imprecise probabilities, including theory and applications reflecting the current state of the art"-- Provided by publisher |
| Bibliography |
Includes bibliographical references and index. |
| Contents |
Machine generated contents note: 1.1. Introduction / Erik Quaeghebeur -- 1.2. Reasoning about and with sets of desirable gambles / Erik Quaeghebeur -- 1.2.1. Rationality criteria / Erik Quaeghebeur -- 1.2.2. Assessments avoiding partial or sure loss / Erik Quaeghebeur -- 1.2.3. Coherent sets of desirable gambles / Erik Quaeghebeur -- 1.2.4. Natural extension / Erik Quaeghebeur -- 1.2.5. Desirability relative to subspaces with arbitrary vector orderings / Erik Quaeghebeur -- 1.3. Deriving and combining sets of desirable gambles / Erik Quaeghebeur -- 1.3.1. Gamble space transformations / Erik Quaeghebeur -- 1.3.2. Derived coherent sets of desirable gambles / Erik Quaeghebeur -- 1.3.3. Conditional sets of desirable gambles / Erik Quaeghebeur -- 1.3.4. Marginal sets of desirable gambles / Erik Quaeghebeur -- 1.3.5. Combining sets of desirable gambles / Erik Quaeghebeur -- 1.4. Partial preference orders / Erik Quaeghebeur -- 1.4.1. Strict preference / Erik Quaeghebeur -- 1.4.2. Nonstrict preference / Erik Quaeghebeur -- 1.4.3. Nonstrict preferences implied by strict ones / Erik Quaeghebeur -- 1.4.4. Strict preferences implied by nonstrict ones / Erik Quaeghebeur -- 1.5. Maximally committal sets of strictly desirable gambles / Erik Quaeghebeur -- 1.6. Relationships with other, nonequivalent models / Erik Quaeghebeur -- 1.6.1. Linear previsions / Erik Quaeghebeur -- 1.6.2. Credal sets / Erik Quaeghebeur -- 1.6.3. To lower and upper previsions / Erik Quaeghebeur -- 1.6.4. Simplified variants of desirability / Erik Quaeghebeur -- 1.6.5. From lower previsions / Erik Quaeghebeur -- 1.6.6. Conditional lower previsions / Erik Quaeghebeur -- 1.7. Further reading / Erik Quaeghebeur -- Acknowledgements / Erik Quaeghebeur -- 2.1. Introduction / Enrique Miranda / Gert de Cooman -- 2.2. Coherent lower previsions / Enrique Miranda / Gert de Cooman -- 2.2.1. Avoiding sure loss and coherence / Gert de Cooman / Enrique Miranda -- 2.2.2. Linear previsions / Enrique Miranda / Gert de Cooman -- 2.2.3. Sets of desirable gambles / Gert de Cooman / Enrique Miranda -- 2.2.4. Natural extension / Enrique Miranda / Gert de Cooman -- 2.3. Conditional lower previsions / Gert de Cooman / Enrique Miranda -- 2.3.1. Coherence of a finite number of conditional lower previsions / Enrique Miranda / Gert de Cooman -- 2.3.2. Natural extension of conditional lower previsions / Gert de Cooman / Enrique Miranda -- 2.3.3. Coherence of an unconditional and a conditional lower prevision / Enrique Miranda / Gert de Cooman -- 2.3.4. Updating with the regular extension / Gert de Cooman / Enrique Miranda -- 2.4. Further reading / Gert de Cooman / Enrique Miranda -- 2.4.1. work of Williams / Gert de Cooman / Enrique Miranda -- 2.4.2. work of Kuznetsov / Enrique Miranda / Gert de Cooman -- 2.4.3. work of Weichselberger / Enrique Miranda / Gert de Cooman -- Acknowledgements / Gert de Cooman / Enrique Miranda -- 3.1. Introduction / Gert de Cooman / Enrique Miranda -- 3.2. Irrelevance and independence / Gert de Cooman / Enrique Miranda -- 3.2.1. Epistemic irrelevance / Gert de Cooman / Enrique Miranda -- 3.2.2. Epistemic independence / Gert de Cooman / Enrique Miranda -- 3.2.3. Envelopes of independent precise models / Gert de Cooman / Enrique Miranda -- 3.2.4. Strong independence / Gert de Cooman / Enrique Miranda -- 3.2.5. formalist approach to independence / Gert de Cooman / Enrique Miranda -- 3.3. Invariance / Gert de Cooman / Enrique Miranda -- 3.3.1. Weak invariance / Gert de Cooman / Enrique Miranda -- 3.3.2. Strong invariance / Gert de Cooman / Enrique Miranda -- 3.4. Exchangeability / Gert de Cooman / Enrique Miranda -- 3.4.1. Representation theorem for finite sequences / Gert de Cooman / Enrique Miranda -- 3.4.2. Exchangeable natural extension / Gert de Cooman / Enrique Miranda -- 3.4.3. Exchangeable sequences / Gert de Cooman / Enrique Miranda -- 3.5. Further reading / Gert de Cooman / Enrique Miranda -- 3.5.1. Independence / Gert de Cooman / Enrique Miranda -- 3.5.2. Invariance / Gert de Cooman / Enrique Miranda -- 3.5.3. Exchangeability / Gert de Cooman / Enrique Miranda -- Acknowledgements / Gert de Cooman / Enrique Miranda -- 4.1. Introduction / Didier Dubois / Sébastien Destercke -- 4.2. Capacities and n-monotonicity / Didier Dubois / Sébastien Destercke -- 4.3. 2-monotone capacities / Didier Dubois / Sébastien Destercke -- 4.4. Probability intervals on singletons / Didier Dubois / Sébastien Destercke -- 4.5. infinity-monotone capacities / Didier Dubois / Sébastien Destercke -- 4.5.1. Constructing infinity-monotone capacities / Didier Dubois / Sébastien Destercke -- 4.5.2. Simple support functions / Didier Dubois / Sébastien Destercke -- 4.5.3. Further elements / Didier Dubois / Sébastien Destercke -- 4.6. Possibility distributions, p-boxes, clouds and related models / Sébastien Destercke / Didier Dubois -- 4.6.1. Possibility distributions / Didier Dubois / Sébastien Destercke -- 4.6.2. Fuzzy intervals / Didier Dubois / Sébastien Destercke -- 4.6.3. Clouds / Didier Dubois / Sébastien Destercke -- 4.6.4. p-boxes / Didier Dubois / Sébastien Destercke -- 4.7. Neighbourhood models / Didier Dubois / Sébastien Destercke -- 4.7.1. Pari-mutuel / Didier Dubois / Sébastien Destercke -- 4.7.2. Odds-ratio / Didier Dubois / Sébastien Destercke -- 4.7.3. Linear-vacuous / Didier Dubois / Sébastien Destercke -- 4.7.4. Relations between neighbourhood models / Didier Dubois / Sébastien Destercke -- 4.8. Summary / Didier Dubois / Sébastien Destercke -- 5.1. Imprecise probability = modal logic + probability / Didier Dubois / Sébastien Destercke -- 5.1.1. Boolean possibility theory and modal logic / Didier Dubois / Sébastien Destercke -- 5.1.2. unifying framework for capacity based uncertainty theories / Didier Dubois / Sébastien Destercke -- 5.2. From imprecise probabilities to belief functions and possibility theory / Didier Dubois / Sébastien Destercke -- 5.2.1. Random disjunctive sets / Didier Dubois / Sébastien Destercke -- 5.2.2. Numerical possibility theory / Didier Dubois / Sébastien Destercke -- 5.2.3. Overall picture / Didier Dubois / Sébastien Destercke -- 5.3. Discrepancies between uncertainty theories / Didier Dubois / Sébastien Destercke -- 5.3.1. Objectivist vs. |
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Contents note continued: 13.5. Hybrid models / Michael Oberguggenberger -- 13.6. Reliability analysis and decision making in engineering / Michael Oberguggenberger -- 13.7. Further reading / Michael Oberguggenberger -- 14.1. Introduction / Lev V. Utkin / Frank P.A. Coolen -- 14.2. Stress-strength reliability / Lev V. Utkin / Frank P.A. Coolen -- 14.3. Statistical inference in reliability and risk / Lev V. Utkin / Frank P.A. Coolen -- 14.4. Nonparametric predictive inference in reliability and risk / Lev V. Utkin / Frank P.A. Coolen -- 14.5. Discussion and research challenges / Lev V. Utkin / Frank P.A. Coolen -- 15.1. Methods and issues / Michael Smithson -- 15.2. Evaluating imprecise probability judgements / Michael Smithson -- 15.3. Factors affecting elicitation / Michael Smithson -- 15.4. Matching methods with purposes / Michael Smithson -- 15.5. Further reading / Michael Smithson -- 16.1. Introduction / Robert Hable / Matthias C.M. Troffaes -- 16.2. Natural extension / Robert Hable / Matthias C.M. Troffaes -- 16.2.1. Conditional lower previsions with arbitrary domains / Robert Hable / Matthias C.M. Troffaes -- 16.2.2. Walley-Pelessoni-Vicig algorithm / Robert Hable / Matthias C.M. Troffaes -- 16.2.3. Choquet integration / Robert Hable / Matthias C.M. Troffaes -- 16.2.4. Möbius inverse / Robert Hable / Matthias C.M. Troffaes -- 16.2.5. Linear-vacuous mixture / Robert Hable / Matthias C.M. Troffaes -- 16.3. Decision making / Robert Hable / Matthias C.M. Troffaes -- 16.3.1. Γ-maximin, Γ-maximax and Hurwicz / Robert Hable / Matthias C.M. Troffaes -- 16.3.2. Maximality / Robert Hable / Matthias C.M. Troffaes -- 16.3.3. E-admissibility / Robert Hable / Matthias C.M. Troffaes -- 16.3.4. Interval dominance / Robert Hable / Matthias C.M. Troffaes. |
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Subjectivist standpoints / Sébastien Destercke / Didier Dubois -- 5.3.2. Discrepancies in conditioning / Sébastien Destercke / Didier Dubois -- 5.3.3. Discrepancies in notions of independence / Sébastien Destercke / Didier Dubois -- 5.3.4. Discrepancies in fusion operations / Sébastien Destercke / Didier Dubois -- 5.4. Further reading / Didier Dubois / Sébastien Destercke -- 6.1. Introduction / Vladimir Vovk / Glenn Shafer -- 6.2. law of large numbers / Glenn Shafer / Vladimir Vovk -- 6.3. general forecasting protocol / Vladimir Vovk / Glenn Shafer -- 6.4. axiom of continuity / Vladimir Vovk / Glenn Shafer -- 6.5. Doob's argument / Vladimir Vovk / Glenn Shafer -- 6.6. Limit theorems of probability / Vladimir Vovk / Glenn Shafer -- 6.7. Lévy's zero-one law / Vladimir Vovk / Glenn Shafer -- 6.8. axiom of continuity revisited / Glenn Shafer / Vladimir Vovk -- 6.9. Further reading / Vladimir Vovk / Glenn Shafer -- Acknowledgements / Vladimir Vovk / Glenn Shafer -- 7.1. Background and introduction / Thomas Augustin / Gero Walter / Frank P.A. Coolen -- 7.1.1. What is statistical inference? / Thomas Augustin / Gero Walter / Frank P.A. Coolen -- 7.1.2. (Parametric) statistical models and i.i.d. samples / Thomas Augustin / Gero Walter / Frank P.A. Coolen -- 7.1.3. Basic tasks and procedures of statistical inference / Thomas Augustin / Gero Walter / Frank P.A. Coolen -- 7.1.4. Some methodological distinctions / Thomas Augustin / Gero Walter / Frank P.A. Coolen -- 7.1.5. Examples: Multinomial and normal distribution / Thomas Augustin / Gero Walter / Frank P.A. Coolen -- 7.2. Imprecision in statistics, some general sources and motives / Thomas Augustin / Gero Walter / Frank P.A. Coolen -- 7.2.1. Model and data imprecision; sensitivity analysis and ontological views on imprecision / Thomas Augustin / Gero Walter / Frank P.A. Coolen -- 7.2.2. robustness shock, sensitivity analysis / Thomas Augustin / Gero Walter / Frank P.A. Coolen -- 7.2.3. Imprecision as a modelling tool to express the quality of partial knowledge / Gero Walter / Frank P.A. Coolen / Thomas Augustin -- 7.2.4. law of decreasing credibility / Thomas Augustin / Gero Walter / Frank P.A. Coolen -- 7.2.5. Imprecise sampling models: Typical models and motives / Thomas Augustin / Gero Walter / Frank P.A. Coolen -- 7.3. Some basic concepts of statistical models relying on imprecise probabilities / Gero Walter / Thomas Augustin / Frank P.A. Coolen -- 7.3.1. Most common classes of models and notation / Thomas Augustin / Gero Walter / Frank P.A. Coolen -- 7.3.2. Imprecise parametric statistical models and corresponding i.i.d. samples / Thomas Augustin / Gero Walter / Frank P.A. Coolen -- 7.4. Generalized Bayesian inference / Thomas Augustin / Gero Walter / Frank P.A. Coolen -- 7.4.1. Some selected results from traditional Bayesian statistics / Gero Walter / Thomas Augustin / Frank P.A. Coolen -- 7.4.2. Sets of precise prior distributions, robust Bayesian inference and the generalized Bayes rule / Thomas Augustin / Gero Walter / Frank P.A. Coolen. |
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Note continued: 7.4.3. closer exemplary look at a popular class of models: The IDM and other models based on sets of conjugate priors in exponential families / Thomas Augustin / Gero Walter / Frank P.A. Coolen -- 7.4.4. Some further comments and a brief look at other models for generalized Bayesian inference / Thomas Augustin / Gero Walter / Frank P.A. Coolen -- 7.5. Frequentist statistics with imprecise probabilities / Thomas Augustin / Gero Walter / Frank P.A. Coolen -- 7.5.1. nonrobustness of classical frequentist methods / Thomas Augustin / Gero Walter / Frank P.A. Coolen -- 7.5.2. (Frequentist) hypothesis testing under imprecise probability: Huber-Strassen theory and extensions / Thomas Augustin / Gero Walter / Frank P.A. Coolen -- 7.5.3. Towards a frequentist estimation theory under imprecise probabilities -- some basic criteria and first results / Thomas Augustin / Gero Walter / Frank P.A. Coolen -- 7.5.4. brief outlook on frequentist methods / Thomas Augustin / Gero Walter / Frank P.A. Coolen -- 7.6. Nonparametric predictive inference / Thomas Augustin / Frank P.A. Coolen / Gero Walter -- 7.6.1. Overview / Thomas Augustin / Frank P.A. Coolen / Gero Walter -- 7.6.2. Applications and challenges / Thomas Augustin / Frank P.A. Coolen / Gero Walter -- 7.7. brief sketch of some further approaches and aspects / Thomas Augustin / Frank P.A. Coolen / Gero Walter -- 7.8. Data imprecision, partial identification / Thomas Augustin / Frank P.A. Coolen / Gero Walter -- 7.8.1. Data imprecision / Thomas Augustin / Frank P.A. Coolen / Gero Walter -- 7.8.2. Cautious data completion / Thomas Augustin / Frank P.A. Coolen / Gero Walter -- 7.8.3. Partial identification and observationally equivalent models / Thomas Augustin / Frank P.A. Coolen / Gero Walter -- 7.8.4. brief outlook on some further aspects / Thomas Augustin / Frank P.A. Coolen / Gero Walter -- 7.9. Some general further reading / Thomas Augustin / Frank P.A. Coolen / Gero Walter -- 7.10. Some general challenges / Thomas Augustin / Frank P.A. Coolen / Gero Walter -- Acknowledgements / Thomas Augustin / Frank P.A. Coolen / Gero Walter -- 8.1. Non-sequential decision problems / Nathan Huntley / Matthias C.M. Troffaes / Robert Hable -- 8.1.1. Choosing from a set of gambles / Nathan Huntley / Matthias C.M. Troffaes / Robert Hable -- 8.1.2. Choice functions for coherent lower previsions / Nathan Huntley / Matthias C.M. Troffaes / Robert Hable -- 8.2. Sequential decision problems / Nathan Huntley / Matthias C.M. Troffaes / Robert Hable -- 8.2.1. Static sequential solutions: Normal form / Nathan Huntley / Matthias C.M. Troffaes / Robert Hable -- 8.2.2. Dynamic sequential solutions: Extensive form / Nathan Huntley / Matthias C.M. Troffaes / Robert Hable -- 8.3. Examples and applications / Robert Hable / Nathan Huntley / Matthias C.M. Troffaes -- 8.3.1. Ellsberg's paradox / Nathan Huntley / Matthias C.M. Troffaes / Robert Hable -- 8.3.2. Robust Bayesian statistics / Nathan Huntley / Matthias C.M. Troffaes / Robert Hable -- 9.1. Introduction / Alessandro Antonucci / Marco Zaffalon / Cassio P. de Campos -- 9.2. Credal sets / Alessandro Antonucci / Marco Zaffalon / Cassio P. de Campos -- 9.2.1. Definition and relation with lower previsions / Alessandro Antonucci / Marco Zaffalon / Cassio P. de Campos -- 9.2.2. Marginalization and conditioning / Alessandro Antonucci / Marco Zaffalon / Cassio P. de Campos -- 9.2.3. Composition / Alessandro Antonucci / Marco Zaffalon / Cassio P. de Campos -- 9.3. Independence / Alessandro Antonucci / Cassio P. de Campos / Marco Zaffalon -- 9.4. Credal networks / Alessandro Antonucci / Marco Zaffalon / Cassio P. de Campos -- 9.4.1. Nonseparately specified credal networks / Alessandro Antonucci / Marco Zaffalon / Cassio P. de Campos -- 9.5. Computing with credal networks / Alessandro Antonucci / Marco Zaffalon / Cassio P. de Campos -- 9.5.1. Credal networks updating / Alessandro Antonucci / Marco Zaffalon / Cassio P. de Campos -- 9.5.2. Modelling and updating with missing data / Alessandro Antonucci / Marco Zaffalon / Cassio P. de Campos -- 9.5.3. Algorithms for credal networks updating / Alessandro Antonucci / Marco Zaffalon / Cassio P. de Campos -- 9.5.4. Inference on credal networks as a multilinear programming task / Alessandro Antonucci / Marco Zaffalon / Cassio P. de Campos -- 9.6. Further reading / Alessandro Antonucci / Marco Zaffalon / Cassio P. de Campos -- Acknowledgements / Alessandro Antonucci / Marco Zaffalon / Cassio P. |
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De Campos -- 10.1. Introduction / Giorgio Corani / Joaquin Abellán / Marco Zaffalon / Serafin Moral / Andrés Masegosa -- 10.2. Naive Bayes / Giorgio Corani / Joaquin Abellán / Marco Zaffalon / Serafin Moral / Andrés Masegosa -- 10.2.1. Derivation of naive Bayes / Joaquin Abellán / Andrés Masegosa / Giorgio Corani / Marco Zaffalon / Serafin Moral -- 10.3. Naive credal classifier (NCC) / Giorgio Corani / Joaquin Abellán / Marco Zaffalon / Serafin Moral / Andrés Masegosa -- 10.3.1. Checking Credal-dominance / Giorgio Corani / Joaquin Abellán / Marco Zaffalon / Serafin Moral / Andrés Masegosa -- 10.3.2. Particular behaviours of NCC / Giorgio Corani / Joaquin Abellán / Marco Zaffalon / Serafin Moral / Andrés Masegosa -- 10.3.3. NCC2: Conservative treatment of missing data / Giorgio Corani / Joaquin Abellán / Marco Zaffalon / Serafin Moral / Andrés Masegosa -- 10.4. Extensions and developments of the naive credal classifier / Giorgio Corani / Joaquin Abellán / Marco Zaffalon / Serafin Moral / Andrés Masegosa -- 10.4.1. Lazy naive credal classifier / Giorgio Corani / Joaquin Abellán / Marco Zaffalon / Serafin Moral / Andrés Masegosa -- 10.4.2. Credal model averaging / Giorgio Corani / Joaquin Abellán / Marco Zaffalon / Serafin Moral / Andrés Masegosa -- 10.4.3. Profile-likelihood classifiers / Giorgio Corani / Joaquin Abellán / Marco Zaffalon / Serafin Moral / Andrés Masegosa -- 10.4.4. Tree-augmented networks (TAN) / Giorgio Corani / Joaquin Abellán / Marco Zaffalon / Serafin Moral / Andrés Masegosa -- 10.5. Tree-based credal classifiers / Giorgio Corani / Joaquin Abellán / Marco Zaffalon / Serafin Moral / Andrés Masegosa -- 10.5.1. Uncertainty measures on credal sets: The maximum entropy function / Giorgio Corani / Joaquin Abellán / Marco Zaffalon / Serafin Moral / Andrés Masegosa -- 10.5.2. Obtaining conditional probability intervals with the imprecise Dirichlet model / Giorgio Corani / Joaquin Abellán / Marco Zaffalon / Serafin Moral / Andrés Masegosa -- 10.5.3. Classification procedure / Giorgio Corani / Joaquin Abellán / Marco Zaffalon / Serafin Moral / Andrés Masegosa -- 10.6. Metrics, experiments and software / Giorgio Corani / Joaquin Abellán / Marco Zaffalon / Serafin Moral / Andrés Masegosa -- 10.7. Scoring the conditional probability of the class / Giorgio Corani / Joaquin Abellán / Marco Zaffalon / Serafin Moral / Andrés Masegosa -- 10.7.1. Software / Giorgio Corani / Joaquin Abellán / Andrés Masegosa / Serafin Moral / Marco Zaffalon -- 10.7.2. Experiments / Marco Zaffalon / Serafin Moral / Andrés Masegosa / Joaquin Abellán / Giorgio Corani -- 10.7.3. Experiments comparing conditional probabilities of the class / Serafin Moral / Marco Zaffalon / Andrés Masegosa / Joaquin Abellán / Giorgio Corani -- Acknowledgements / Serafin Moral / Andrés Masegosa / Joaquin Abellán / Giorgio Corani / Marco Zaffalon -- 11.1. classical characterization of stochastic processes / Filip Herman / Damjan [Š]kluj -- 11.1.1. Basic definitions / Filip Herman / Damjan [Š]kluj -- 11.1.2. Precise Markov chains / Filip Herman / Damjan [Š]kluj -- 11.2. Event-driven random processes / Filip Herman / Damjan [Š]kluj -- 11.3. Imprecise Markov chains / Filip Herman / Damjan [Š]kluj -- 11.3.1. From precise to imprecise Markov chains / Filip Herman / Damjan [Š]kluj -- 11.3.2. Imprecise Markov models under epistemic irrelevance / Filip Herman / Damjan [Š]kluj -- 11.3.3. Imprecise Markov models under strong independence / Filip Herman / Damjan [Š]kluj -- 11.3.4. When does the interpretation of independence (not) matter? / Filip Herman / Damjan [Š]kluj -- 11.4. Limit behaviour of imprecise Markov chains / Filip Herman / Damjan [Š]kluj -- 11.4.1. Metric properties of imprecise probability models / Filip Herman / Damjan [Š]kluj -- 11.4.2. Perron-Frobenius theorem / Filip Herman / Damjan [Š]kluj -- 11.4.3. Invariant distributions / Filip Herman / Damjan [Š]kluj -- 11.4.4. Coefficients of ergodicity / Filip Herman / Damjan [Š]kluj -- 11.4.5. Coefficients of ergodicity for imprecise Markov chains / Filip Herman / Damjan [Š]kluj -- 11.5. Further reading / Damjan [Š]kluj / Filip Herman -- 12.1. Introduction / Paolo Vicig -- 12.2. Imprecise previsions and betting / Paolo Vicig -- 12.3. Imprecise previsions and risk measurement / Paolo Vicig -- 12.3.1. Risk measures as imprecise previsions / Paolo Vicig -- 12.3.2. Coherent risk measures / Paolo Vicig -- 12.3.3. Convex risk measures (and previsions) / Paolo Vicig -- 12.4. Further reading / Paolo Vicig -- 13.1. Introduction / Michael Oberguggenberger -- 13.2. Probabilistic dimensioning in a simple example / Michael Oberguggenberger -- 13.3. Random set modelling of the output variability / Michael Oberguggenberger -- 13.4. Sensitivity analysis / Michael Oberguggenberger. |
| Subject |
Probabilities.
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Probabilités. |
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probability. |
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Probabilities |
| Added Author |
Augustin, Thomas, editor.
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| Other Form: |
Print version: Introduction to imprecise probabilities. Hoboken, NJ : John Wiley & Sons Inc., 2014 9780470973813 (DLC) 2013041146 (OCoLC)851413880 |
| ISBN |
9781118763148 (ePub) |
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1118763149 (ePub) |
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9781118763131 (Adobe PDF) |
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1118763130 (Adobe PDF) |
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9781118763117 |
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1118763114 |
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(hardback) |
| Music No. |
EB00378991 Recorded Books |
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