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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 theory, probability distribution, as developed by Andrey Kolmogorov, Kolmogorov, Pierre-Simon Laplace, Laplace, Bruno de Finetti, de Finetti, Frank P. Ramsey, Ramsey, Richard Threlkeld Cox, Cox, Dennis Lindley, Lindley, and many others. However, this has not been unani ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Theory
Probability theory or probability calculus 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 of probability, axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure (mathematics), 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 (probability theory), event. Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes (which provide mathematical abstractions of determinism, non-deterministic or uncertain processes or measured Quantity, quantities that may either be single occurrences or evolve over time in a random fashion). Although it is no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Maynard Keynes
John Maynard Keynes, 1st Baron Keynes ( ; 5 June 1883 – 21 April 1946), was an English economist and philosopher whose ideas fundamentally changed the theory and practice of macroeconomics and the economic policies of governments. Originally trained in mathematics, he built on and greatly refined earlier work on the causes of business cycles. One of the most influential economists of the 20th century, he produced writings that are the basis for the schools of economic thought, school of thought known as Keynesian economics, and its various offshoots. His ideas, reformulated as New Keynesianism, are fundamental to mainstream economics, mainstream macroeconomics. He is known as the "father of macroeconomics". During the Great Depression of the 1930s, Keynes spearheaded Keynesian Revolution, a revolution in economic thinking, challenging the ideas of neoclassical economics that held that free markets would, in the short to medium term, automatically provide full employment, as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Mathematical Analysis And Applications
The ''Journal of Mathematical Analysis and Applications'' is an academic journal in mathematics, specializing in mathematical analysis and related topics in applied mathematics. It was founded in 1960 by Richard Bellman, as part of a series of new journals on areas of mathematics published by Academic Press, and is now published by Elsevier. For most years since 2003 it has been ranked by SCImago Journal Rank The SCImago Journal Rank (SJR) indicator is a measure of the prestige of scholarly journals that accounts for both the number of citations received by a journal and the prestige of the journals where the citations come from. Etymology SCImago ... as among the top 25% of journals in its topic areas. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Choquet Integral
A Choquet integral is a subadditive or superadditive integral created by the French mathematician Gustave Choquet in 1953. It was initially used in statistical mechanics and potential theory, but found its way into decision theory in the 1980s, where it is used as a way of measuring the expected utility of an uncertain event. It is applied specifically to membership functions and capacities. In imprecise probability theory, the Choquet integral is also used to calculate the lower expectation induced by a 2-monotone lower probability, or the upper expectation induced by a 2-alternating upper probability. Using the Choquet integral to denote the expected utility of belief functions measured with capacities is a way to reconcile the Ellsberg paradox and the Allais paradox. Multiobjective optimization problems seek Pareto optimal solutions, but the Pareto set of such solutions can be extremely large, especially with multiple objectives. To manage this, optimization often focus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-parametric Statistics
Nonparametric statistics is a type of statistical analysis that makes minimal assumptions about the underlying distribution of the data being studied. Often these models are infinite-dimensional, rather than finite dimensional, as in parametric statistics. Nonparametric statistics can be used for descriptive statistics or statistical inference. Nonparametric tests are often used when the assumptions of parametric tests are evidently violated. Definitions The term "nonparametric statistics" has been defined imprecisely in the following two ways, among others: The first meaning of ''nonparametric'' involves techniques that do not rely on data belonging to any particular parametric family of probability distributions. These include, among others: * Methods which are ''distribution-free'', which do not rely on assumptions that the data are drawn from a given parametric family of probability distributions. * Statistics defined to be a function on a sample, without dependency on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robust Statistics
Robust statistics are statistics that maintain their properties even if the underlying distributional assumptions are incorrect. Robust Statistics, statistical methods have been developed for many common problems, such as estimating location parameter, location, scale parameter, scale, and regression coefficient, regression parameters. One motivation is to produce statistical methods that are not unduly affected by outliers. Another motivation is to provide methods with good performance when there are small departures from a Parametric statistics, parametric distribution. For example, robust methods work well for mixtures of two normal distributions with different standard deviations; under this model, non-robust methods like a t-test work poorly. Introduction Robust statistics seek to provide methods that emulate popular statistical methods, but are not unduly affected by outliers or other small departures from Statistical assumption, model assumptions. In statistics, classical e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peter Walley
Peter may refer to: People * List of people named Peter, a list of people and fictional characters with the given name * Peter (given name) ** Saint Peter (died 60s), apostle of Jesus, leader of the early Christian Church * Peter (surname), a surname (including a list of people with the name) Culture * Peter (actor) (born 1952), stage name Shinnosuke Ikehata, a Japanese dancer and actor * ''Peter'' (1934 film), a film directed by Henry Koster * ''Peter'' (2021 film), a Marathi language film * "Peter" (''Fringe'' episode), an episode of the television series ''Fringe'' * ''Peter'' (novel), a 1908 book by Francis Hopkinson Smith * "Peter" (short story), an 1892 short story by Willa Cather * ''Peter'' (album), a 1972 album by Peter Yarrow * ''Peter'', a 1993 EP by Canadian band Eric's Trip * "Peter", 2024 song by Taylor Swift from '' The Tortured Poets Department: The Anthology'' Animals * Peter (Lord's cat), cat at Lord's Cricket Ground in London * Peter (chief mouser), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Teddy Seidenfeld
Teddy Seidenfeld is an American statistician and philosopher currently the H. A. Simon University Professor at Carnegie Mellon University Carnegie Mellon University (CMU) is a private research university in Pittsburgh, Pennsylvania, United States. The institution was established in 1900 by Andrew Carnegie as the Carnegie Technical Schools. In 1912, it became the Carnegie Institu .... References Year of birth missing (living people) Living people Carnegie Mellon University faculty American philosophers {{US-philosopher-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isaac Levi
Isaac Levi (June 30, 1930 – December 25, 2018) was an American philosopher who served as the John Dewey Professor of Philosophy at Columbia University. He is noted for his work in epistemology and decision theory. Education and career Levi was one of several doctoral students of Ernest Nagel at Columbia University who were influential in American post-war philosophy; others were Morton White, Patrick Suppes, and Henry E. Kyburg, Jr. Levi taught at Case Western Reserve University before joining the Columbia faculty in 1970. He was elected in 1986 to the American Academy of Arts and Sciences. Levi also served as doctoral advisor to prominent formal philosophers, including Horacio Arló-Costa and Teddy Seidenfeld, and acted as a mentor to Cheryl Misak during her year at Columbia. There was a debate between Kyburg and Levi on topics in what has come to be known as formal epistemology. Philosophical work Levi first made a name for himself with his first book, ''Gambling with T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Henry Kyburg
Henry E. Kyburg Jr. (1928–2007) was Gideon Burbank Professor of Moral Philosophy and Professor of Computer Science at the University of Rochester, New York, and Pace Eminent Scholar at the Institute for Human and Machine Cognition, Pensacola, Florida. His first faculty posts were at Rockefeller Institute, University of Denver, Wesleyan College, and Wayne State University. Kyburg worked in probability and logic, and is known for his Lottery Paradox (1961). Kyburg also edited ''Studies in Subjective Probability'' (1964) with Howard Smokler. Because of this collection's relation to Bayesian probability, Kyburg is often misunderstood to be a Bayesian. His own theory of probability is outlined in ''Logical Foundations of Statistical Inference'' (1974), a theory that first found form in his 1961 book ''Probability and the Logic of Rational Belief'' (in turn, a work closely related to his doctoral thesis). Kyburg describes his theory as Keynesian and Fisherian (see John Maynard K ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peter M
Peter may refer to: People * List of people named Peter, a list of people and fictional characters with the given name * Peter (given name) ** Saint Peter (died 60s), apostle of Jesus, leader of the early Christian Church * Peter (surname), a surname (including a list of people with the name) Culture * Peter (actor) (born 1952), stage name Shinnosuke Ikehata, a Japanese dancer and actor * ''Peter'' (1934 film), a film directed by Henry Koster * ''Peter'' (2021 film), a Marathi language film * "Peter" (''Fringe'' episode), an episode of the television series ''Fringe'' * ''Peter'' (novel), a 1908 book by Francis Hopkinson Smith * "Peter" (short story), an 1892 short story by Willa Cather * ''Peter'' (album), a 1972 album by Peter Yarrow * ''Peter'', a 1993 EP by Canadian band Eric's Trip * "Peter", 2024 song by Taylor Swift from '' The Tortured Poets Department: The Anthology'' Animals * Peter (Lord's cat), cat at Lord's Cricket Ground in London * Peter (chief mouser), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Glenn Shafer
Glenn Shafer (born November 21, 1946) is an American mathematician and statistician. He is the co-creator of Dempster–Shafer theory. He is a University Professor and Board of Governors Professor at Rutgers University. Early life and education Shafer grew up on a farm near Caney, Kansas. He received a bachelor's degree in mathematics from Princeton University, then entered the Peace Corps, serving in Afghanistan. He returned to Princeton, earning a PhD in mathematical statistics in 1973 under Geoffrey Watson. Career He taught at Princeton and the University of Kansas, joining the faculty of Rutgers Business School – Newark and New Brunswick in 1992. From 2011 to 2014 he served as dean of the school. During the 1970s and 1980s he expanded a theory first introduced by Arthur P. Dempster to create Dempster–Shafer theory, also described as the theory of belief functions or evidence theory. It is a general framework for reasoning with uncertainty, allowing one to combine evi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
