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Leonard J. Savage
Leonard Jimmie Savage (born Leonard Ogashevitz; 1917 – 1971) was an American mathematician and statistician. Economist Milton Friedman said Savage was "one of the few people I have met whom I would unhesitatingly call a genius." Education and career Savage was born and grew up in Detroit. He studied at Wayne State University in Detroit before transferring to University of Michigan, where he first majored in chemical engineering, then switched to mathematics, graduating in 1938 with a bachelor's degree. He continued at the University of Michigan with a PhD on differential geometry in 1941 under the supervision of Sumner Byron Myers. Savage subsequently worked at the Institute for Advanced Study in Princeton, New Jersey, the University of Chicago, the University of Michigan, Yale University, and the Statistical Research Group at Columbia University. Though his thesis advisor was Sumner Myers, he also credited Milton Friedman and W. Allen Wallis as statistical mentors. During ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Detroit
Detroit ( , ) is the List of municipalities in Michigan, most populous city in the U.S. state of Michigan. It is situated on the bank of the Detroit River across from Windsor, Ontario. It had a population of 639,111 at the 2020 United States census, 2020 census, making it the List of United States cities by population, 26th-most populous city in the United States and the largest U.S. city on the Canada–United States border. The Metro Detroit area, home to 4.3 million people, is the second-largest in the Midwestern United States, Midwest after the Chicago metropolitan area and the 14th-largest in the United States. The county seat, seat of Wayne County, Michigan, Wayne County, Detroit is a significant cultural center known for its contributions to music, art, architecture and design, in addition to its historical automotive and industrial background. In 1701, Kingdom of France, Royal French explorers Antoine de la Mothe Cadillac and Alphonse de Tonty founded Fort Pontc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Savage's Subjective Expected Utility Model
In decision theory, Savage's subjective expected utility model (also known as Savage's framework, Savage's axioms, or Savage's representation theorem) is a formalization of subjective expected utility (SEU) developed by Leonard J. Savage in his 1954 book ''The Foundations of Statistics'', based on previous work by Ramsey, von Neumann and de Finetti. Savage's model concerns with deriving a subjective probability distribution and a utility function such that an agent's choice under uncertainty can be represented via expected-utility maximization. His contributions to the theory of SEU consist of formalizing a framework under which such problem is well-posed, and deriving conditions for its positive solution. Primitives and problem Savage's framework posits the following primitives to represent an agent's choice under uncertainty: * A set of ''states of the world'' \Omega, of which only one \omega \in \Omega is true. The agent does not know the true \omega, so \Omega ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Institute For Advanced Study
The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Einstein, J. Robert Oppenheimer, Emmy Noether, Hermann Weyl, John von Neumann, Michael Walzer, Clifford Geertz and Kurt Gödel, many of whom had emigrated from Europe to the United States. It was founded in 1930 by American educator Abraham Flexner, together with philanthropists Louis Bamberger and Caroline Bamberger Fuld. Despite collaborative ties and neighboring geographic location, the institute, being independent, has "no formal links" with Princeton University. The institute does not charge tuition or fees. Flexner's guiding principle in founding the institute was the pursuit of knowledge for its own sake.Jogalekar. The faculty have no classes to teach. There are no degree programs or experimental facilities at the institute. Research ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Geometry
Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as classical antiquity, antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Nikolai Lobachevsky, Lobachevsky. The simplest examples of smooth spaces are the Differential geometry of curves, plane and space curves and Differential geometry of surfaces, surfaces in the three-dimensional Euclidean space, and the study of these shapes formed the basis for development of modern differential geometry during the 18th and 19th centuries. Since the late 19th century, differential geometry has grown into a field concerned more generally with geometric structures on differentiable ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wayne State University
Wayne State University (WSU) is a public university, public research university in Detroit, Michigan, United States. Founded in 1868, Wayne State consists of 13 schools and colleges offering approximately 375 programs. It is Michigan's third-largest university with nearly 24,000 graduate and undergraduate students. Wayne State University, along with the University of Michigan and Michigan State University, compose the University Research Corridor of Michigan. Wayne State is Carnegie Classification of Institutions of Higher Education, classified among "R1: Doctoral Universities – Very high research activity". Wayne State's main campus comprises 203 acres linking more than 100 education and research buildings. It also has three satellite campuses in Macomb and Wayne counties. The Wayne State Warriors compete in the NCAA Division II Great Lakes Intercollegiate Athletic Conference (GLIAC). History Wayne State University was established in 1868 as the Detroit Medical College by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Milton Friedman
Milton Friedman (; July 31, 1912 – November 16, 2006) was an American economist and statistician who received the 1976 Nobel Memorial Prize in Economic Sciences for his research on consumption analysis, monetary history and theory and the complexity of stabilization policy. With George Stigler, Friedman was among the intellectual leaders of the Chicago school of economics, a neoclassical school of economic thought associated with the faculty at the University of Chicago that rejected Keynesianism in favor of monetarism before shifting their focus to new classical macroeconomics in the mid-1970s. Several students, young professors and academics who were recruited or mentored by Friedman at Chicago went on to become leading economists, including Gary Becker, Robert Fogel, and Robert Lucas Jr. Friedman's challenges to what he called "naive Keynesian theory" began with his interpretation of consumption, which tracks how consumers spend. He introduced a theory w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Statisticians
This list of statisticians lists people who have made notable contributions to the theories or application of statistics, or to the related fields of probability or machine learning. It includes the founders of statistics and others. It includes some 17th- and 18th-century mathematicians and polymaths whose work is regarded as influential in shaping the later discipline of statistics. Also included are various actuaries, economist An economist is a professional and practitioner in the social sciences, social science discipline of economics. The individual may also study, develop, and apply theories and concepts from economics and write about economic policy. Within this ...s, and demographers known for providing leadership in applying statistics to their fields. __NOTOC__ A * Aalen, Odd Olai * Abbey, Helen (1915–2001) * Abbott, Edith (1876–1957) * Abelson, Robert P. (1928–2005) * Abramovitz, Moses (1912–2000) * Achenwall, Gottfried (1719–1772) * Adelst ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians was Thales of Miletus (); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales's theorem. The number of known mathematicians grew when Pythagoras of Samos () established the Pythagorean school, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sure-thing Principle
In decision theory, the sure-thing principle states that a decision maker who decided they would take a certain action in the case that event ''E'' has occurred, as well as in the case that the negation of ''E'' has occurred, should also take that same action if they know nothing about ''E''. The principle was coined by L.J. Savage:Savage, L. J. (1954), ''The foundations of statistics''. John Wiley & Sons Inc., New York. Savage formulated the principle as a dominance principle, but it can also be framed probabilistically. Richard Jeffrey and later Judea Pearl showed that Savage's principle is only valid when the probability of the event considered (e.g., the winner of the election) is unaffected by the action (buying the property). Under such conditions, the sure-thing principle is a theorem in the ''do''-calculus (see Bayes networks). Blyth constructed a counterexample to the sure-thing principle using sequential sampling in the context of Simpson's paradox, but this example v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subjective Expected Utility
In decision theory, subjective expected utility (SEU) is a framework for modeling how individuals make choices under uncertainty. In particular, it posits that decision-makers have 1) a subjective probability distribution over uncertain states of the world; and 2) a utility function over consequences such that their choice behavior can be described as maximizing expected utility over consequences with respect to their subjective probability. This way, the theory of subjective expected utility combines two subjective concepts: a personal utility function, and a personal probability distribution (usually based on Bayesian probability theory). SEU is a different approach from the one put forward by von Neumann and Morgenstern in that it does not take (objecive) probabilities (i.e., lotteries) as given. Instead, subjective probabilities are used, which are assumed to be consistent with choice behavior. The main contribution to formalizing SEU was done by L. J. Savage in 1954 (see ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regret (decision Theory)
In decision theory, regret aversion (or anticipated regret) describes how the human emotional response of regret can influence decision-making under uncertainty. When individuals make choices without complete information, they often experience regret if they later discover that a different choice would have produced a better outcome. This regret can be quantified as the difference in value between the actual decision made and what would have been the optimal decision in hindsight. Unlike traditional models that consider regret as merely a post-decision emotional response, the theory of regret aversion proposes that decision-makers actively anticipate potential future regret and incorporate this anticipation into their current decision-making process. This anticipation can lead individuals to make choices specifically designed to minimize the possibility of experiencing regret later, even if those choices are not optimal from a purely probabilistic expected-value perspective. Regre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Likelihood Principle
In statistics, the likelihood principle is the proposition that, given a statistical model, all the evidence in a sample relevant to model parameters is contained in the likelihood function. A likelihood function arises from a probability density function considered as a function of its distributional parameterization argument. For example, consider a model which gives the probability density function \; f_X(x \mid \theta)\; of observable random variable \, X \, as a function of a parameter \,\theta~. Then for a specific value \,x\, of \,X~, the function \,\mathcal(\theta \mid x) = f_X(x \mid \theta)\; is a likelihood function of \,\theta~: it gives a measure of how "likely" any particular value of \,\theta\, is, if we know that \,X\, has the value \,x~. The density function may be a density with respect to counting measure, i.e. a probability mass function. Two likelihood functions are ''equivalent'' if one is a scalar multiple of the other. The likelihood princip ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
