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Dempster–Shafer Theory
The theory of belief functions, also referred to as evidence theory or Dempster–Shafer theory (DST), is a general framework for reasoning with uncertainty, with understood connections to other frameworks such as probability, possibility and imprecise probability theories. First introduced by Arthur P. Dempster in the context of statistical inference, the theory was later developed by Glenn Shafer into a general framework for modeling epistemic uncertainty—a mathematical theory of evidence.Shafer, Glenn; ''A Mathematical Theory of Evidence'', Princeton University Press, 1976, The theory allows one to combine evidence from different sources and arrive at a degree of belief (represented by a mathematical object called ''belief function'') that takes into account all the available evidence. In a narrow sense, the term Dempster–Shafer theory refers to the original conception of the theory by Dempster and Shafer. However, it is more common to use the term in the wider sense of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dempster In Brest
Dempster may refer to: * Dempster (surname), a surname * Dempster Woodworth, Wisconsin state senator and physician * Dempster (deemster) – an official at pre-1746 baronial courts' moot hills in Scotland. * Dempster, South Dakota * Dempster Land District, Western Australia * Dempster Highway, a Canadian roadway, in the Yukon and Northwest Territories * Dempster Street, a major east–west artery north of Chicago, Illinois, part of which is part of U.S. Route 14 ** Dempster (CTA Purple Line station), a Chicago Transit Authority rapid transit station in Evanston, Illinois ** Dempster-Skokie (CTA station), a Chicago Transit Authority rapid transit station in Skokie, Illinois ** Dempster Street station (C&NW), a former commuter rail station in Evanston, Illinois * Dempster Brothers, Inc., a Tennessee industrial firm ** Dempster Dumpmaster, a garbage-handling vehicle manufactured by the company ** Dempster Dumpster, a waste receptacle manufactured by the company * Dempster's brand bread ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Checksum
A checksum is a small-sized block of data derived from another block of digital data for the purpose of detecting errors that may have been introduced during its transmission or storage. By themselves, checksums are often used to verify data integrity but are not relied upon to verify data authenticity. The procedure which generates this checksum is called a checksum function or checksum algorithm. Depending on its design goals, a good checksum algorithm usually outputs a significantly different value, even for small changes made to the input. This is especially true of cryptographic hash functions, which may be used to detect many data corruption errors and verify overall data integrity; if the computed checksum for the current data input matches the stored value of a previously computed checksum, there is a very high probability the data has not been accidentally altered or corrupted. Checksum functions are related to hash functions, fingerprints, randomization functions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joseph Halpern
Joseph Yehuda Halpern (born 1953) is an Israeli-American professor of computer science at Cornell University. Most of his research is on reasoning about knowledge and uncertainty. Biography Halpern graduated in 1975 from University of Toronto with a B.S. in mathematics. He went on to earn a Ph.D. in mathematics from Harvard University in 1981 under the supervision of Albert R. Meyer and Gerald Sacks. He has written three books, ''Actual Causality'', ''Reasoning about Uncertainty,'' and ''Reasoning About Knowledge'' and is a winner of the 1997 Gödel Prize in theoretical computer science and the 2009 Dijkstra Prize in distributed computing. From 1997 to 2003 he was editor-in-chief of the Journal of the ACM. In 2002 he was inducted as a Fellow of the Association for Computing Machinery and in 2012 he was selected as an IEEE Fellow. In 2011 he was awarded a Senior Fellowship of the Zukunftskolleg at the University of Konstanz. In 2019, Halpern was elected a member of the National ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical Consequence
Logical consequence (also entailment) is a fundamental concept in logic, which describes the relationship between statements that hold true when one statement logically ''follows from'' one or more statements. A valid logical argument is one in which the conclusion is entailed by the premises, because the conclusion is the consequence of the premises. The philosophical analysis of logical consequence involves the questions: In what sense does a conclusion follow from its premises? and What does it mean for a conclusion to be a consequence of premises?Beall, JC and Restall, Greg, Logical Consequence' The Stanford Encyclopedia of Philosophy (Fall 2009 Edition), Edward N. Zalta (ed.). All of philosophical logic is meant to provide accounts of the nature of logical consequence and the nature of logical truth. Logical consequence is necessary and formal, by way of examples that explain with formal proof and models of interpretation. A sentence is said to be a logical conse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Empty Set
In mathematics, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic set theories ensure that the empty set exists by including an axiom of empty set, while in other theories, its existence can be deduced. Many possible properties of sets are vacuously true for the empty set. Any set other than the empty set is called non-empty. In some textbooks and popularizations, the empty set is referred to as the "null set". However, null set is a distinct notion within the context of measure theory, in which it describes a set of measure zero (which is not necessarily empty). The empty set may also be called the void set. Notation Common notations for the empty set include "", "\emptyset", and "∅". The latter two symbols were introduced by the Bourbaki group (specifically André Weil) in 1939, inspired by the letter Ø in the Danish and Norwegian alphabets. In the past, "0" was occasionally used as a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Universe (mathematics)
In mathematics, and particularly in set theory, category theory, type theory, and the foundations of mathematics, a universe is a collection that contains all the entities one wishes to consider in a given situation. In set theory, universes are often classes that contain (as elements) all sets for which one hopes to prove a particular theorem. These classes can serve as inner models for various axiomatic systems such as ZFC or Morse–Kelley set theory. Universes are of critical importance to formalizing concepts in category theory inside set-theoretical foundations. For instance, the canonical motivating example of a category is Set, the category of all sets, which cannot be formalized in a set theory without some notion of a universe. In type theory, a universe is a type whose elements are types. In a specific context Perhaps the simplest version is that ''any'' set can be a universe, so long as the object of study is confined to that particular set. If the object of st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Knightian Uncertainty
In economics, Knightian uncertainty is a lack of any quantifiable knowledge about some possible occurrence, as opposed to the presence of quantifiable risk (e.g., that in statistical noise or a parameter's confidence interval). The concept acknowledges some fundamental degree of ignorance, a limit to knowledge, and an essential unpredictability of future events. Knightian uncertainty is named after University of Chicago economist Frank Knight (1885–1972), who distinguished risk and uncertainty in his 1921 work ''Risk, Uncertainty, and Profit:''Knight, F. H. (1921Risk, Uncertainty, and Profit Boston, MA: Hart, Schaffner & Marx; Houghton Mifflin Company :"Uncertainty must be taken in a sense radically distinct from the familiar notion of Risk, from which it has never been properly separated.... The essential fact is that 'risk' means in some cases a quantity susceptible of measurement, while at other times it is something distinctly not of this character; and there are far-re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arrovian Uncertainty
In economics, Knightian uncertainty is a lack of any quantifiable knowledge about some possible occurrence, as opposed to the presence of quantifiable risk (e.g., that in statistical noise or a parameter's confidence interval). The concept acknowledges some fundamental degree of ignorance, a limit to knowledge, and an essential unpredictability of future events. Knightian uncertainty is named after University of Chicago economist Frank Knight (1885–1972), who distinguished risk and uncertainty in his 1921 work ''Risk, Uncertainty, and Profit:''Knight, F. H. (1921Risk, Uncertainty, and Profit Boston, MA: Hart, Schaffner & Marx; Houghton Mifflin Company :"Uncertainty must be taken in a sense radically distinct from the familiar notion of Risk, from which it has never been properly separated.... The essential fact is that 'risk' means in some cases a quantity susceptible of measurement, while at other times it is something distinctly not of this character; and there are far-rea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Howard Raiffa
Howard Raiffa (; January 24, 1924 – July 8, 2016) was an American academic who was the Frank P. Ramsey Professor (Emeritus) of Managerial Economics, a joint chair held by the Business School and Harvard Kennedy School at Harvard University. He was an influential Bayesian decision theorist and pioneer in the field of decision analysis, with works in statistical decision theory, game theory, behavioral decision theory, risk analysis, and negotiation analysis. He helped found and was the first director of the International Institute for Applied Systems Analysis. Early life After service in the Army Air Forces during World War II, Raiffa received a bachelor's degree in mathematics in 1946, a master's degree in statistics in 1947 and a PhD in mathematics in 1951, all from the University of Michigan. Career *His book ''Applied Statistical Decision Theory'' with Robert Schlaifer introduced the idea of conjugate prior distributions. *A lecture of his in the 1960s concerning the use o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ellsberg's Paradox
In decision theory, the Ellsberg paradox (or Ellsberg's paradox) is a paradox in which people's decisions are inconsistent with subjective expected utility theory. Daniel Ellsberg popularized the paradox in his 1961 paper, “Risk, Ambiguity, and the Savage Axioms”. John Maynard Keynes published a version of the paradox in 1921. It is generally taken to be evidence of ambiguity aversion, in which a person tends to prefer choices with quantifiable risks over those with unknown, incalculable risks. Ellsberg's findings indicate that choices with an underlying level of risk are favored in instances where the likelihood of risk is clear, rather than instances in which the likelihood of risk is unknown. A decision-maker will overwhelmingly favor a choice with a transparent likelihood of risk, even in instances where the unknown alternative will likely produce greater utility. When offered choices with varying risk, people prefer choices with calculable risk, even when they have less ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ignorance
Ignorance is a lack of knowledge and understanding. The word "ignorant" is an adjective that describes a person in the state of being unaware, or even cognitive dissonance and other cognitive relation, and can describe individuals who are unaware of important information or facts. Ignorance can appear in three different types: factual ignorance (absence of knowledge of some fact), object ignorance (unacquaintance with some object), and technical ignorance (absence of knowledge of how to do something). Consequences Ignorance can have negative effects on individuals and societies, but can also benefit them by creating within them the desire to know more. For example, ignorance within science opens the opportunity to seek knowledge and make discoveries by asking new questions. Though this can only take place if the individual possesses a curious mind. Studies suggest that adults with an adequate education who perform enriching and challenging jobs are happier, and more in control of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Risk
In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty about the effects/implications of an activity with respect to something that humans value (such as health, well-being, wealth, property or the environment), often focusing on negative, undesirable consequences. Many different definitions have been proposed. The international standard definition of risk for common understanding in different applications is “effect of uncertainty on objectives”. The understanding of risk, the methods of assessment and management, the descriptions of risk and even the definitions of risk differ in different practice areas (business, economics, environment, finance, information technology, health, insurance, safety, security etc). This article provides links to more detailed articles on these areas. The international standard for risk management, ISO 31000, provides principles and generic guidelines on managing risks faced by organizations. Definitions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
