Introduction to imprecise probabilities /

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"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 de...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Otros Autores: Augustin, Thomas (Editor )
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Chichester, West Sussex : John Wiley & Sons Inc., 2014.
Temas:
Probabilities.
Probabilités.
probability.
MATHEMATICS > Probability & Statistics > General.
Probabilities
Acceso en línea:Texto completo
Texto completo
Tabla de Contenidos:
  • 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.
  • 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.
  • 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.
  • 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.

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