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001433068 001__ 1433068
001433068 003__ OCoLC
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001433068 019__ $$a1227449661$$a1233071915$$a1236895138$$a1238205181
001433068 020__ $$a9783030631536$$q(electronic bk.)
001433068 020__ $$a3030631532$$q(electronic bk.)
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001433068 020__ $$z9783030631529
001433068 0247_ $$a10.1007/978-3-030-63153-6$$2doi
001433068 035__ $$aSP(OCoLC)1228039541
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001433068 08204 $$a003/.54$$223
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001433068 1001_ $$aCuzzolin, Fabio.
001433068 24514 $$aThe geometry of uncertainty :$$bthe geometry of imprecise probabilities /$$cFabio Cuzzolin.
001433068 260__ $$aCham :$$bSpringer,$$c2021.
001433068 300__ $$a1 online resource (864 pages)
001433068 336__ $$atext$$btxt$$2rdacontent
001433068 337__ $$acomputer$$bc$$2rdamedia
001433068 338__ $$aonline resource$$bcr$$2rdacarrier
001433068 347__ $$atext file
001433068 347__ $$bPDF
001433068 4901_ $$aArtificial Intelligence: Foundations, Theory, and Algorithms
001433068 500__ $$a3.2.4 Pearl's criticism.
001433068 504__ $$aIncludes bibliographical references.
001433068 5050_ $$aIntro -- Preface -- Uncertainty -- Probability -- Beyond probability -- Belief functions -- Aim(s) of the book -- Structure and topics -- Acknowledgements -- Table of Contents -- 1 Introduction -- 1.1 Mathematical probability -- 1.2 Interpretations of probability -- 1.2.1 Does probability exist at all? -- 1.2.2 Competing interpretations -- 1.2.3 Frequentist probability -- 1.2.4 Propensity -- 1.2.5 Subjective and Bayesian probability -- 1.2.6 Bayesian versus frequentist inference -- 1.3 Beyond probability -- 1.3.1 Something is wrong with probability Flaws of the frequentistic setting
001433068 5058_ $$a1.3.2 Pure data: Beware of the prior -- 1.3.3 Pure data: Designing the universe? -- 1.3.4 No data: Modelling ignorance -- 1.3.5 Set-valued observations: The cloaked die -- 1.3.6 Propositional data -- 1.3.7 Scarce data: Beware the size of the sample -- 1.3.8 Unusual data: Rare events -- 1.3.9 Uncertain data -- 1.3.10 Knightian uncertainty -- 1.4 Mathematics (plural) of uncertainty -- 1.4.1 Debate on uncertainty theory -- 1.4.2 Belief, evidence and probability -- Part I Theories of uncertainty -- 2 Belief functions -- Chapter outline -- 2.1 Arthur Dempster's original setting
001433068 5058_ $$a2.2 Belief functions as set functions -- 2.2.1 Basic definitions Basic probability assignments Definition 4. -- 2.2.2 Plausibility and commonality functions -- 2.2.3 Bayesian belief functions -- 2.3 Dempster's rule of combination -- 2.3.1 Definition -- 2.3.2 Weight of conflict -- 2.3.3 Conditioning belief functions -- 2.4 Simple and separable support functions -- 2.4.1 Heterogeneous and conflicting evidence -- 2.4.2 Separable support functions -- 2.4.3 Internal conflict -- 2.4.4 Inverting Dempster's rule: The canonical decomposition -- 2.5 Families of compatible frames of discernment
001433068 5058_ $$a2.5.1 Refinings -- 2.5.2 Families of frames -- 2.5.3 Consistent and marginal belief functions -- 2.5.4 Independent frames -- 2.5.5 Vacuous extension -- 2.6 Support functions -- 2.6.1 Families of compatible support functions in the evidential language -- 2.6.2 Discerning the relevant interaction of bodies of evidence -- 2.7 Quasi-support functions -- 2.7.1 Limits of separable support functions -- 2.7.2 Bayesian belief functions as quasi-support functions -- 2.7.3 Bayesian case: Bayes' theorem -- 2.7.4 Bayesian case: Incompatible priors -- 2.8 Consonant belief functions
001433068 5058_ $$a3 Understanding belief functions -- Chapter outline -- 3.1 The multiple semantics of belief functions -- 3.1.1 Dempster's multivalued mappings, compatibility relations -- 3.1.2 Belief functions as generalised (non-additive) probabilities -- 3.1.3 Belief functions as inner measures -- 3.1.4 Belief functions as credal sets -- 3.1.5 Belief functions as random sets -- 3.1.6 Behavioural interpretations -- 3.1.7 Common misconceptions Belief -- 3.2 Genesis and debate -- 3.2.1 Early support -- 3.2.2 Constructive probability and Shafer's canonical examples -- 3.2.3 Bayesian versus belief reasoning
001433068 506__ $$aAccess limited to authorized users.
001433068 520__ $$aThe principal aim of this book is to introduce to the widest possible audience an original view of belief calculus and uncertainty theory. In this geometric approach to uncertainty, uncertainty measures can be seen as points of a suitably complex geometric space, and manipulated in that space, for example, combined or conditioned. In the chapters in Part I, Theories of Uncertainty, the author offers an extensive recapitulation of the state of the art in the mathematics of uncertainty. This part of the book contains the most comprehensive summary to date of the whole of belief theory, with Chap. 4 outlining for the first time, and in a logical order, all the steps of the reasoning chain associated with modelling uncertainty using belief functions, in an attempt to provide a self-contained manual for the working scientist. In addition, the book proposes in Chap. 5 what is possibly the most detailed compendium available of all theories of uncertainty. Part II, The Geometry of Uncertainty, is the core of this book, as it introduces the author's own geometric approach to uncertainty theory, starting with the geometry of belief functions: Chap. 7 studies the geometry of the space of belief functions, or belief space, both in terms of a simplex and in terms of its recursive bundle structure; Chap. 8 extends the analysis to Dempster's rule of combination, introducing the notion of a conditional subspace and outlining a simple geometric construction for Dempster's sum; Chap. 9 delves into the combinatorial properties of plausibility and commonality functions, as equivalent representations of the evidence carried by a belief function; then Chap. 10 starts extending the applicability of the geometric approach to other uncertainty measures, focusing in particular on possibility measures (consonant belief functions) and the related notion of a consistent belief function. The chapters in Part III, Geometric Interplays, are concerned with the interplay of uncertainty measures of different kinds, and the geometry of their relationship, with a particular focus on the approximation problem. Part IV, Geometric Reasoning, examines the application of the geometric approach to the various elements of the reasoning chain illustrated in Chap. 4, in particular conditioning and decision making. Part V concludes the book by outlining a future, complete statistical theory of random sets, future extensions of the geometric approach, and identifying high-impact applications to climate change, machine learning and artificial intelligence. The book is suitable for researchers in artificial intelligence, statistics, and applied science engaged with theories of uncertainty. The book is supported with the most comprehensive bibliography on belief and uncertainty theory.
001433068 588__ $$aDescription based on print version record.
001433068 650_0 $$aUncertainty (Information theory)
001433068 650_0 $$aArtificial intelligence.
001433068 650_0 $$aStatistics.
001433068 650_0 $$aProbabilities.
001433068 650_6 $$aIncertitude (Théorie de l'information)
001433068 650_6 $$aIntelligence artificielle.
001433068 650_6 $$aProbabilités.
001433068 655_0 $$aElectronic books.
001433068 77608 $$iPrint version:$$aCuzzolin, Fabio.$$tGeometry of Uncertainty : The Geometry of Imprecise Probabilities.$$dCham : Springer International Publishing AG, ©2021$$z9783030631529
001433068 830_0 $$aArtificial Intelligence: Foundations, Theory, and Algorithms.
001433068 852__ $$bebk
001433068 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-030-63153-6$$zOnline Access$$91397441.1
001433068 909CO $$ooai:library.usi.edu:1433068$$pGLOBAL_SET
001433068 980__ $$aBIB
001433068 980__ $$aEBOOK
001433068 982__ $$aEbook
001433068 983__ $$aOnline
001433068 994__ $$a92$$bISE