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Info-gap Decision Theory
Info-gap decision theory seeks to optimize robustness to failure under severe uncertainty,Yakov Ben-Haim, ''Information-Gap Theory: Decisions Under Severe Uncertainty,'' Academic Press, London, 2001.Yakov Ben-Haim, ''Info-Gap Theory: Decisions Under Severe Uncertainty,'' 2nd edition, Academic Press, London, 2006. in particular applying sensitivity analysis of the stability radius type to perturbations in the value of a given estimate of the parameter of interest. It has some connections with Wald's maximin model; some authors distinguish them, others consider them instances of the same principle. It was developed by Yakov Ben-Haim, and has found many applications and described as a theory for decision-making under "''severe'' uncertainty". It has been criticized as unsuited for this purpose, and alternatives proposed, including such classical approaches as robust optimization. Applications Info-gap theory has generated a lot of literature. Info-gap theory has been studied o ... [...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] |
Black Swan Theory
The black swan theory or theory of black swan events is a metaphor that describes an event that comes as a surprise, has a major effect, and is often inappropriately rationalized after the fact with the benefit of hindsight. The term arose from a Latin expression which was based on the presumption that black swans did not exist. The expression was used in the original manner until around 1697 when Dutch mariners saw black swans living in Australia. After this, the term was reinterpreted to mean an unforeseen and consequential event. The reinterpreted theory was articulated by Nassim Nicholas Taleb, starting in 2001, to explain: # The disproportionate role of high-profile, hard-to-predict, and rare events that are beyond the realm of normal expectations in history, science, finance, and technology. # The non-computability of the probability of consequential rare events using scientific methods (owing to the very nature of small probabilities). # The psychological biases that bl ... [...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- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayesian Probability
Bayesian probability ( or ) is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification of a personal belief. The Bayesian interpretation of probability can be seen as an extension of propositional logic that enables reasoning with hypotheses; that is, with propositions whose truth or falsity is unknown. In the Bayesian view, a probability is assigned to a hypothesis, whereas under frequentist inference, a hypothesis is typically tested without being assigned a probability. Bayesian probability belongs to the category of evidential probabilities; to evaluate the probability of a hypothesis, the Bayesian probabilist specifies a prior probability. This, in turn, is then updated to a posterior probability in the light of new, relevant data (evidence). The Bayesian interpretation provides a standard set of procedur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Criticism Of Info-gap Decision Theory
Info-gap decision theory seeks to optimize robustness to failure under severe uncertainty,Yakov Ben-Haim, ''Information-Gap Theory: Decisions Under Severe Uncertainty,'' Academic Press, London, 2001.Yakov Ben-Haim, ''Info-Gap Theory: Decisions Under Severe Uncertainty,'' 2nd edition, Academic Press, London, 2006. in particular applying sensitivity analysis of the stability radius type to perturbations in the value of a given estimate of the parameter of interest. It has some connections with Wald's maximin model; some authors distinguish them, others consider them instances of the same principle. It was developed by Yakov Ben-Haim, and has found many applications and described as a theory for decision-making under "''severe'' uncertainty". It has been criticized as unsuited for this purpose, and alternatives proposed, including such classical approaches as robust optimization. Applications Info-gap theory has generated a lot of literature. Info-gap theory has been studied o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complete Class Theorems
In statistics, completeness is a property of a statistic computed on a sample dataset in relation to a parametric model of the dataset. It is opposed to the concept of an ancillary statistic. While an ancillary statistic contains no information about the model parameters, a complete statistic contains only information about the parameters, and no ancillary information. It is closely related to the concept of a sufficient statistic which contains all of the information that the dataset provides about the parameters. Definition Consider a random variable ''X'' whose probability distribution belongs to a parametric model ''P''''θ'' parametrized by ''θ''. Say ''T'' is a statistic; that is, the composition of a measurable function with a random sample ''X''1,...,''X''n. The statistic ''T'' is said to be complete for the distribution of ''X'' if, for every measurable function ''g,'' :\text\operatorname_\theta(g(T))=0\text\theta\text\mathbf_\theta(g(T)=0)=1\text\theta. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Mathematical Probabilists
:''See probabilism for the followers of such a theory in theology or philosophy''. {{ProbabilityTopicsTOC This list contains only probabilists in the sense of mathematicians specializing in probability theory. * David Aldous (born 1952) * Siva Athreya (born 1971) *Thomas Bayes (1702–1761) - British mathematician and Presbyterian minister, known for Bayes' theorem * Gerard Ben-Arous (born 1957) - Courant Institute of Mathematical Sciences * Itai Benjamini *Jakob Bernoulli (1654–1705) - Switzerland, known for Bernoulli trials *Joseph Louis François Bertrand (1822–1900) * Abram Samoilovitch Besicovitch (1891–1970) * Patrick Billingsley (1925–2011) * Erwin Bolthausen (born 1945) * Carlo Emilio Bonferroni (1892–1960) *Émile Borel (1871–1956) *Sourav Chatterjee (born 1979) * Kai Lai Chung (1917–2009) * Erhan Çınlar (born 1941) *Harald Cramér (1893–1985) * Amir Dembo (born 1958) *Persi Diaconis (born 1945) *Hugo Duminil-Copin (born 1985) * Joseph Leo Doob (1910–20 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Principle Of Insufficient Reason
The principle of indifference (also called principle of insufficient reason) is a rule for assigning epistemic probabilities. The principle of indifference states that in the absence of any relevant evidence, agents should distribute their credence (or "degrees of belief") equally among all the possible outcomes under consideration. In Bayesian probability, this is the simplest non-informative prior. Examples The textbook examples for the application of the principle of indifference are coins, dice, and cards. In a macroscopic system, at least, it must be assumed that the physical laws that govern the system are not known well enough to predict the outcome. As observed some centuries ago by John Arbuthnot (in the preface of ''Of the Laws of Chance'', 1692), :It is impossible for a Die, with such determin'd force and direction, not to fall on such determin'd side, only I don't know the force and direction which makes it fall on such determin'd side, and therefore I call it Ch ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maximin (decision Theory)
Minimax (sometimes Minmax, MM or saddle point) is a decision rule used in artificial intelligence, decision theory, combinatorial game theory, statistics, and philosophy for ''minimizing'' the possible loss for a worst case (''max''imum loss) scenario. When dealing with gains, it is referred to as "maximin" – to maximize the minimum gain. Originally formulated for several-player zero-sum game theory, covering both the cases where players take alternate moves and those where they make simultaneous moves, it has also been extended to more complex games and to general decision-making in the presence of uncertainty. Game theory In general games The maximin value is the highest value that the player can be sure to get without knowing the actions of the other players; equivalently, it is the lowest value the other players can force the player to receive when they know the player's action. Its formal definition is: :\underline = \max_ \min_ Where: * is the index of the play ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abraham Wald
Abraham Wald (; ; , ; – ) was a Hungarian and American mathematician and statistician who contributed to decision theory, geometry and econometrics, and founded the field of sequential analysis. One of his well-known statistical works was written during World War II on how to minimize the damage to bomber aircraft and took into account the survivorship bias in his calculations. He spent his research career at Columbia University. He was the grandson of Rabbi Moshe Shmuel Glasner. Life and career Wald was born on 31 October 1902 in Cluj-Napoca, Kolozsvár, Transylvania, in the Kingdom of Hungary. A religious Jew, he did not attend school on Saturdays, as was then required by the Hungarian school system, and so he was homeschooled by his parents until college. His parents were quite knowledgeable and competent as teachers. In 1928, he graduated in mathematics from the Babeș-Bolyai University, King Ferdinand I University. In 1927, he had entered Postgraduate education, g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sensitivity Analysis
Sensitivity analysis is the study of how the uncertainty in the output of a mathematical model or system (numerical or otherwise) can be divided and allocated to different sources of uncertainty in its inputs. This involves estimating sensitivity indices that quantify the influence of an input or group of inputs on the output. A related practice is uncertainty analysis, which has a greater focus on uncertainty quantification and propagation of uncertainty; ideally, uncertainty and sensitivity analysis should be run in tandem. Motivation A mathematical model (for example in biology, climate change, economics, renewable energy, agronomy...) can be highly complex, and as a result, its relationships between inputs and outputs may be faultily understood. In such cases, the model can be viewed as a black box, i.e. the output is an "opaque" function of its inputs. Quite often, some or all of the model inputs are subject to sources of uncertainty, including errors of measurement, er ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minimax
Minimax (sometimes Minmax, MM or saddle point) is a decision rule used in artificial intelligence, decision theory, combinatorial game theory, statistics, and philosophy for ''minimizing'' the possible loss function, loss for a Worst-case scenario, worst case (''max''imum loss) scenario. When dealing with gains, it is referred to as "maximin" – to maximize the minimum gain. Originally formulated for several-player zero-sum game theory, covering both the cases where players take alternate moves and those where they make simultaneous moves, it has also been extended to more complex games and to general decision-making in the presence of uncertainty. Game theory In general games The maximin value is the highest value that the player can be sure to get without knowing the actions of the other players; equivalently, it is the lowest value the other players can force the player to receive when they know the player's action. Its formal definition is: :\underline = \max_ \min_ W ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
