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Upper And Lower Probabilities
Upper and lower probabilities are representations of imprecise probability. Whereas probability theory uses a single number, the probability, to describe how likely an event is to occur, this method uses two numbers: the upper probability of the event and the lower probability of the event. Because frequentist statistics disallows metaprobabilities, frequentists have had to propose new solutions. Cedric Smith and Arthur Dempster each developed a theory of upper and lower probabilities. Glenn Shafer developed Dempster's theory further, and it is now known as Dempster–Shafer theory or Choquet (1953). More precisely, in the work of these authors one considers in a power set, P(S)\,\!, a ''mass'' function m : P(S)\rightarrow R satisfying the conditions :m(\varnothing) = 0 \,\,\,\,\,\,\! ; \,\,\,\,\,\, m(A) \ge 0 \,\,\,\,\,\,\! ; \,\,\,\,\,\, \sum_ m(A) = 1. \,\! In turn, a mass is associated with two non-additive continuous measures called belief and plausibility defined as fol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Imprecise Probability
Imprecise probability generalizes probability theory to allow for partial probability specifications, and is applicable when information is scarce, vague, or conflicting, in which case a unique probability distribution may be hard to identify. Thereby, the theory aims to represent the available knowledge more accurately. Imprecision is useful for dealing with expert elicitation, because: * People have a limited ability to determine their own subjective probabilities and might find that they can only provide an interval. * As an interval is compatible with a range of opinions, the analysis ought to be more convincing to a range of different people. Introduction Uncertainty is traditionally modelled by a probability distribution, as developed by Kolmogorov, Laplace, de Finetti, Ramsey, Cox, Lindley, and many others. However, this has not been unanimously accepted by scientists, statisticians, and probabilists: it has been argued that some modification or broadening of probabili ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Possibility Measure
Possibility is the condition or fact of being possible. Latin origins of the word hint at ability. Possibility may refer to: * Probability, the measure of the likelihood that an event will occur * Epistemic possibility, a topic in philosophy and modal logic * Possibility theory, a mathematical theory for dealing with certain types of uncertainty and is an alternative to probability theory * Subjunctive possibility, (also called alethic possibility) is a form of modality studied in modal logic. ** Logical possibility, a proposition that will depend on the system of logic being considered, rather than on the violation of any single rule * Possible world, a complete and consistent way the world is or could have been Other *Possible (Italy), a political party in Italy * Possible Peru, a political party in Peru *Possible Peru Alliance, an electoral alliance in Peru Entertainment *''Kim Possible'', a US children's TV series :* Kim Possible (character), the central characte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annals Of Statistics
The ''Annals of Statistics'' is a peer-reviewed statistics journal published by the Institute of Mathematical Statistics. It was started in 1973 as a continuation in part of the '' Annals of Mathematical Statistics (1930)'', which was split into the ''Annals of Statistics'' and the ''Annals of Probability''. The journal CiteScore is 5.8, and its SCImago Journal Rank is 5.877, both from 2020. Articles older than 3 years are available on JSTOR, and all articles since 2004 are freely available on the arXiv. Editorial board The following persons have been editors of the journal: * Ingram Olkin (1972–1973) * I. Richard Savage (1974–1976) * Rupert Miller (1977–1979) * David V. Hinkley (1980–1982) * Michael D. Perlman (1983–1985) * Willem van Zwet (1986–1988) * Arthur Cohen (1988–1991) * Michael Woodroofe (1992–1994) * Larry Brown and John Rice (1995–1997) * Hans-Rudolf Künsch and James O. Berger (1998–2000) * John Marden and Jon A. Wellner (2001–2003) * M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
AAAI Conference On Artificial Intelligence
The AAAI Conference on Artificial Intelligence (AAAI) is one of the leading international academic conference in artificial intelligence held annually. Along with ICML, NeurIPS and ICLR, it is one of the primary conferences of high impact in machine learning and artificial intelligence research. It is supported by the Association for the Advancement of Artificial Intelligence. Precise dates vary from year to year, but paper submissions are generally due at the end of August to beginning of September, and the conference is generally held during the following February. The first AAAI was held in 1980 at Stanford University, Stanford California. During AAAI-20 conference, AI pioneers and 2018 Turing Award winners Yann LeCun and Yoshua Bengio among eight other researchers were honored as the AAAI 2020 Fellows. Along with other conferences such as NeurIPS, ICML, AAAI uses artificial intelligence algorithm to assign papers to reviewers. Locations * AAAI-2023 Washington Convention Ce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Artificial Intelligence (journal)
''Artificial Intelligence'' is a scientific journal on artificial intelligence research. It was established in 1970 and is published by Elsevier. The journal is abstracted and indexed in Scopus and Science Citation Index. The 2021 Impact Factor for this journal is 14.05 and the 5-Year Impact Factor is 11.616.Journal Citation Reports ''Journal Citation Reports'' (''JCR'') is an annual publicationby Clarivate Analytics (previously the intellectual property of Thomson Reuters). It has been integrated with the Web of Science and is accessed from the Web of Science-Core Collect ... 2022, Published by Thomson Reuters References Artificial intelligence publications Computer science journals Elsevier academic journals Publications established in 1970 External links Official website {{compu-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annales De L'Institut Fourier
The ''Annales de l'Institut Fourier'' is a French mathematical journal publishing papers in all fields of mathematics. It was established in 1949. The journal publishes one volume per year, consisting of six issues. The current editor-in-chief is Hervé Pajot. Articles are published either in English or in French. The journal is indexed in ''Mathematical Reviews'', ''Zentralblatt MATH'' and the Web of Science. According to the ''Journal Citation Reports'', the journal had a 2008 impact factor of 0.804. 2008 Journal Citation Reports, Science Edition, Thomson Scientific Thomson Scientific was one of the six (later five) strategic business units of The Thomson Corporation, beginning in 2007, after being separated from Thomson Scientific & Healthcare. Following the merger of Thomson with Reuters Group to form Thom ..., 2008. References External links * Mathematics journals Academic journals established in 1949 Multilingual journals Bimonthly journals Open access journals ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Bounds Analysis
Probability bounds analysis (PBA) is a collection of methods of uncertainty propagation for making qualitative and quantitative calculations in the face of uncertainties of various kinds. It is used to project partial information about random variables and other quantities through mathematical expressions. For instance, it computes sure bounds on the distribution of a sum, product, or more complex function, given only sure bounds on the distributions of the inputs. Such bounds are called probability boxes, and constrain cumulative probability distributions (rather than densities or mass functions). This bounding approach permits analysts to make calculations without requiring overly precise assumptions about parameter values, dependence among variables, or even distribution shape. Probability bounds analysis is essentially a combination of the methods of standard interval analysis and classical probability theory. Probability bounds analysis gives the same answer as interval ana ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interval Finite Element
In numerical analysis, the interval finite element method (interval FEM) is a finite element method that uses interval parameters. Interval FEM can be applied in situations where it is not possible to get reliable probabilistic characteristics of the structure. This is important in concrete structures, wood structures, geomechanics, composite structures, biomechanics and in many other areas. The goal of the Interval Finite Element is to find upper and lower bounds of different characteristics of the model (e.g. stress, displacements, yield surface etc.) and use these results in the design process. This is so called worst case design, which is closely related to the limit state design. Worst case design requires less information than probabilistic design however the results are more conservative Elishakoff.html" ;"title="öylüoglu and Elishakoff">öylüoglu and Elishakoff 1998 Applications of the interval parameters to the modeling of uncertainty Consider the following ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fuzzy Measure Theory
In mathematics, fuzzy measure theory considers generalized measures in which the additive property is replaced by the weaker property of monotonicity. The central concept of fuzzy measure theory is the fuzzy measure (also ''capacity'', see ), which was introduced by Choquet in 1953 and independently defined by Sugeno in 1974 in the context of fuzzy integrals. There exists a number of different classes of fuzzy measures including plausibility/belief measures; possibility/necessity measures; and probability measures, which are a subset of classical measures. Definitions Let \mathbf be a universe of discourse, \mathcal be a class of subsets of \mathbf, and E,F\in\mathcal. A function g:\mathcal\to\mathbb where # \emptyset \in \mathcal \Rightarrow g(\emptyset)=0 # E \subseteq F \Rightarrow g(E)\leq g(F) is called a ''fuzzy measure''. A fuzzy measure is called ''normalized'' or ''regular'' if g(\mathbf)=1. Properties of fuzzy measures A fuzzy measure is: * additive if for an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Possibility Theory
Possibility theory is a mathematical theory for dealing with certain types of uncertainty and is an alternative to probability theory. It uses measures of possibility and necessity between 0 and 1, ranging from impossible to possible and unnecessary to necessary, respectively. Professor Lotfi Zadeh first introduced possibility theory in 1978 as an extension of his theory of fuzzy sets and fuzzy logic. Didier Dubois and Henri Prade further contributed to its development. Earlier in the 1950s, economist G. L. S. Shackle proposed the min/max algebra to describe degrees of potential surprise. Formalization of possibility For simplicity, assume that the universe of discourse Ω is a finite set. A possibility measure is a function \operatorname from 2^\Omega to , 1such that: :Axiom 1: \operatorname(\varnothing) = 0 :Axiom 2: \operatorname(\Omega) = 1 :Axiom 3: \operatorname(U \cup V) = \max \left( \operatorname(U), \operatorname(V) \right) for any disjoint subsets U and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Necessity Measure
Necessary or necessity may refer to: * Need ** An action somebody may feel they must do ** An important task or essential thing to do at a particular time or by a particular moment * Necessary and sufficient condition, in logic, something that is a required condition for something else to be the case * Necessary proposition, in logic, a statement about facts that is either unassailably true (tautology) or obviously false (contradiction) * Metaphysical necessity, in philosophy, a truth which is true in all possible worlds * Necessity in modal logic * Necessity good in economics ;Law * Doctrine of necessity, a concept in constitutional law * Military necessity, a concept in international law * Necessity (criminal law), a defence in criminal law * Necessity (tort), a concept in the law of tort * A necessity in contract law ;Other * , a poem by Letitia Elizabeth Landon being part of ''Three Extracts from the Diary of a Week'', 1837. * "Necessary" (song), by Every Little T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Theory
Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of the sample space is called an event. Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes (which provide mathematical abstractions of non-deterministic or uncertain processes or measured quantities that may either be single occurrences or evolve over time in a random fashion). Although it is not possible to perfectly predict random events, much can be said about their behavior. Two major results in probability ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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