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Bruno De Finetti
Bruno de Finetti (13 June 1906 – 20 July 1985) was an Italian probabilist statistician and actuary, noted for the "operational subjective" conception of probability. The classic exposition of his distinctive theory is the 1937 "La prévision: ses lois logiques, ses sources subjectives," which discussed probability founded on the coherence of betting odds and the consequences of exchangeability. Life De Finetti was born in Innsbruck, Austria, and studied mathematics at Politecnico di Milano. He graduated in 1927 writing his thesis under the supervision of Giulio Vivanti. After graduation, he worked as an actuary and a statistician at ''Istituto Nazionale di Statistica'' ( National Institute of Statistics) in Rome and, from 1931, the Trieste insurance company Assicurazioni Generali. In 1936 he won a competition for Chair of Financial Mathematics and Statistics, but was not nominated due to a fascist law barring access to unmarried candidates; he was appointed as ordinary profess ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Innsbruck
Innsbruck (; bar, Innschbruck, label=Austro-Bavarian ) is the capital of Tyrol and the fifth-largest city in Austria. On the River Inn, at its junction with the Wipp Valley, which provides access to the Brenner Pass to the south, it had a population of 132,493 in 2018. In the broad valley between high mountains, the so-called North Chain in the Karwendel Alps ( Hafelekarspitze, ) to the north and Patscherkofel () and Serles () to the south, Innsbruck is an internationally renowned winter sports centre; it hosted the 1964 and 1976 Winter Olympics as well as the 1984 and 1988 Winter Paralympics. It also hosted the first Winter Youth Olympics in 2012. The name means "bridge over the Inn". History Antiquity The earliest traces suggest initial inhabitation in the early Stone Age. Surviving pre-Roman place names show that the area has been populated continuously. In the 4th century the Romans established the army station Veldidena (the name survives in today's urban dis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Analysis
Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (mathematics), series, and analytic functions. These theories are usually studied in the context of Real number, real and Complex number, complex numbers and Function (mathematics), functions. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis. Analysis may be distinguished from geometry; however, it can be applied to any Space (mathematics), space of mathematical objects that has a definition of nearness (a topological space) or specific distances between objects (a metric space). History Ancient Mathematical analysis formally developed in the 17th century during the Scientific Revolution, but many of its ideas can be traced back to earlier mathematicians. Early results in analysis were i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coherence (philosophical Gambling Strategy)
In a thought experiment proposed by the Italian probabilist Bruno de Finetti in order to justify Bayesian probability, an array of wagers is coherent precisely if it does not expose the wagerer to certain loss regardless of the outcomes of events on which they are wagering, even if their opponent makes the most judicious choices. Operational subjective probabilities as wagering odds One must set the price of a promise to pay $1 if John Smith wins tomorrow's election, and $0 otherwise. One knows that one's opponent will be able to choose either to buy such a promise from one at the price one has set, or require one to buy such a promise from them, still at the same price. In other words: Player A sets the odds, but Player B decides which side of the bet to take. The price one sets is the "operational subjective probability" that one assigns to the proposition on which one is betting. If one decides that John Smith is 12.5% likely to win—an arbitrary valuation—one might then ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thought Experiment
A thought experiment is a hypothetical situation in which a hypothesis, theory, or principle is laid out for the purpose of thinking through its consequences. History The ancient Greek ''deiknymi'' (), or thought experiment, "was the most ancient pattern of mathematical proof", and existed before Euclidean mathematics, where the emphasis was on the conceptual, rather than on the experimental part of a thought-experiment. Johann Witt-Hansen established that Hans Christian Ørsted was the first to use the German term ' (lit. thought experiment) circa 1812. Ørsted was also the first to use the equivalent term ' in 1820. By 1883 Ernst Mach used the term ' in a different way, to denote exclusively the conduct of a experiment that would be subsequently performed as a by his students. Physical and mental experimentation could then be contrasted: Mach asked his students to provide him with explanations whenever the results from their subsequent, real, physical experiment differed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Predictive Inference
Statistical inference is the process of using data analysis to infer properties of an underlying distribution of probability.Upton, G., Cook, I. (2008) ''Oxford Dictionary of Statistics'', OUP. . Inferential statistical analysis infers properties of a population, for example by testing hypotheses and deriving estimates. It is assumed that the observed data set is sampled from a larger population. Inferential statistics can be contrasted with descriptive statistics. Descriptive statistics is solely concerned with properties of the observed data, and it does not rest on the assumption that the data come from a larger population. In machine learning, the term ''inference'' is sometimes used instead to mean "make a prediction, by evaluating an already trained model"; in this context inferring properties of the model is referred to as ''training'' or ''learning'' (rather than ''inference''), and using a model for prediction is referred to as ''inference'' (instead of ''prediction'') ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dennis Lindley
Dennis Victor Lindley (25 July 1923 – 14 December 2013) was an English statistician, decision theorist and leading advocate of Bayesian statistics. Biography Lindley grew up in the south-west London suburb of Surbiton. He was an only child and his father was a local building contractor. Lindley recalled (to Adrian Smith) that the family had "little culture" and that both his parents were "proud of the fact that they had never read a book." The school Lindley attended, Tiffin School, introduced him to "ordinary cultural activities.""The Lindley Prize – Dennis V. Lindley" International Society for ...
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Bayesian Inference
Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. Bayesian inference is an important technique in statistics, and especially in mathematical statistics. Bayesian updating is particularly important in the dynamic analysis of a sequence of data. Bayesian inference has found application in a wide range of activities, including science, engineering, philosophy, medicine, sport, and law. In the philosophy of decision theory, Bayesian inference is closely related to subjective probability, often called "Bayesian probability". Introduction to Bayes' rule Formal explanation Bayesian inference derives the posterior probability as a consequence of two antecedents: a prior probability and a "likelihood function" derived from a statistical model for the observed data. Bayesian inference computes the posterior probability according to Bayes' theorem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radical Party (Italy)
The Radical Party ( it, Partito Radicale, PR) was a liberal and libertarian political party in Italy. For decades, the Radical Party was a bastion of anti-clericalism, civil libertarianism, feminism, liberalism and radicalism in Italy as well as environmentalism. The party proposed itself as the strongest opposition to the Italian political establishment, seen as corrupt and conservative. Although it never reached high shares of vote and never participated in government, the party had close relations with the other parties of the Italian left—from the Republicans and the Socialists to the Communists and Proletarian Democracy—and opened its ranks also to members of other parties through dual membership. The party's longtime leader was Marco Pannella (1930–2016), who served as a member of the Chamber of Deputies (1976–1994) and the European Parliament (1979–2009), leading the party in most of the elections it contested. In 1989, the PR was transformed into the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Christian Socialism
Christian socialism is a religious and political philosophy that blends Christianity and socialism, endorsing left-wing politics and socialist economics on the basis of the Bible and the teachings of Jesus. Many Christian socialists believe capitalism to be idolatrous and rooted in the sin of greed. Christian socialists identify the cause of social inequality to be the greed that they associate with capitalism. Christian socialism became a major movement in the United Kingdom beginning in the 19th century. The Christian Socialist Movement, known as Christians on the Left since 2013, is one formal group, as well as a faction of the Labour Party. According to the Encyclopædia Britannica, socialism is a "social and economic doctrine that calls for public rather than private ownership or control of property and natural resources. According to the socialist view, individuals do not live or work in isolation but live in cooperation with one another. Furthermore, everything that pe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fascism
Fascism is a far-right, authoritarian, ultra-nationalist political ideology and movement,: "extreme militaristic nationalism, contempt for electoral democracy and political and cultural liberalism, a belief in natural social hierarchy and the rule of elites, and the desire to create a (German: “people’s community”), in which individual interests would be subordinated to the good of the nation" characterized by a dictatorial leader, centralized autocracy, militarism, forcible suppression of opposition, belief in a natural social hierarchy, subordination of individual interests for the perceived good of the nation and race, and strong regimentation of society and the economy. Fascism rose to prominence in early 20th-century Europe. The first fascist movements emerged in Italy during World War I, before spreading to other European countries, most notably Germany. Fascism also had adherents outside of Europe. Opposed to anarchism, democracy, pluralism, liberalism ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pareto Efficiency
Pareto efficiency or Pareto optimality is a situation where no action or allocation is available that makes one individual better off without making another worse off. The concept is named after Vilfredo Pareto (1848–1923), Italian civil engineer and economist, who used the concept in his studies of economic efficiency and income distribution. The following three concepts are closely related: * Given an initial situation, a Pareto improvement is a new situation where some agents will gain, and no agents will lose. * A situation is called Pareto-dominated if there exists a possible Pareto improvement. * A situation is called Pareto-optimal or Pareto-efficient if no change could lead to improved satisfaction for some agent without some other agent losing or, equivalently, if there is no scope for further Pareto improvement. The Pareto front (also called Pareto frontier or Pareto set) is the set of all Pareto-efficient situations. Pareto originally used the word "optimal" fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bernard Koopman
Bernard Osgood Koopman (January 19, 1900 – August 18, 1981) was a French-born American mathematician, known for his work in ergodic theory, the foundations of probability, statistical theory and operations research. Education and work After living in France and Italy, Koopman emigrated to the United States in 1915. Koopman was a student of George David Birkhoff and his initial work concentrated on dynamical systems and mathematical physics. In 1931/1932, Koopman and John von Neumann proposed a Hilbert space formulation of classical mechanics, known as the Koopman–von Neumann classical mechanics. During World War II, he joined the Anti-Submarine Warfare Operations Research Group (ASWORG, later ORG) in Washington, D.C., directed by Philip M. Morse, to work for the U.S. Navy.Philip M. Morse: ''In memoriam: Bernard Osgood Koopman, 1900–1981'', Operations Research, Vol. 30, No. 3 (May - Jun., 1982), pp. viii+417-427. Published by: Institute for Operations Research and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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