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Markov Chain Monte Carlo
In statistics, Markov chain Monte Carlo (MCMC) is a class of algorithms used to draw samples from a probability distribution. Given a probability distribution, one can construct a Markov chain whose elements' distribution approximates it – that is, the Markov chain's Discrete-time Markov chain#Stationary distributions, equilibrium distribution matches the target distribution. The more steps that are included, the more closely the distribution of the sample matches the actual desired distribution. Markov chain Monte Carlo methods are used to study probability distributions that are too complex or too highly N-dimensional space, dimensional to study with analytic techniques alone. Various algorithms exist for constructing such Markov chains, including the Metropolis–Hastings algorithm. General explanation Markov chain Monte Carlo methods create samples from a continuous random variable, with probability density proportional to a known function. These samples can be used to e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics
Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of statistical survey, surveys and experimental design, experiments. When census data (comprising every member of the target population) cannot be collected, statisticians collect data by developing specific experiment designs and survey sample (statistics), samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistically Independent
Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes. Two event (probability theory), events are independent, statistically independent, or stochastically independent if, informally speaking, the occurrence of one does not affect the probability of occurrence of the other or, equivalently, does not affect the odds. Similarly, two random variables are independent if the realization of one does not affect the probability distribution of the other. When dealing with collections of more than two events, two notions of independence need to be distinguished. The events are called Pairwise independence, pairwise independent if any two events in the collection are independent of each other, while mutual independence (or collective independence) of events means, informally speaking, that each event is independent of any combination of other events in the collection. A similar notion exists for collections of random variables. M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Donald Geman
Donald Jay Geman (born September 20, 1943) is an American applied mathematician and a leading researcher in the field of machine learning and pattern recognition. He and his brother, Stuart Geman, are very well known for proposing the Gibbs sampler and for the first proof of the convergence of the simulated annealing algorithm, in an article that became a highly cited reference in engineering (over 21K citations according to Google Scholar, as of January 2018). He is a professor at the Johns Hopkins University and simultaneously a visiting professor at École Normale Supérieure de Cachan. Biography Geman was born in Chicago in 1943. He graduated from the University of Illinois Urbana-Champaign in 1965 with a B.A. degree in English Literature and from Northwestern University in 1970 with a Ph.D. in mathematics. His dissertation was entitled as "Horizontal-window conditioning and the zeros of stationary processes." He joined University of Massachusetts - Amherst in 1970, wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stuart Geman
Stuart Alan Geman (born March 23, 1949) is an American mathematician, known for influential contributions to computer vision, statistics, probability theory, machine learning, and the neurosciences. ikipediaList of important publications in computer science. He and his brother, Donald Geman, are well known for proposing the Gibbs sampler, and for the first proof of convergence of the simulated annealing algorithm. Biography Geman was born and raised in Chicago. He was educated at the University of Michigan (B.S., Physics, 1971), Dartmouth Medical College (MS, Neurophysiology, 1973), and the Massachusetts Institute of Technology (Ph.D, Applied Mathematics, 1977). Since 1977, he has been a member of the faculty at Brown University, where he has worked in the Pattern Theory group, and is currently the James Manning Professor of Applied Mathematics. He has received many honors and awards, including selection as a Presidential Young Investigator and as an ISI Highly Cited researc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Julian Besag
Julian Ernst Besag Fellow of the Royal Society, FRS (26 March 1945 – 6 August 2010) was a British statistician known chiefly for his work in spatial statistics (including its applications to epidemiology, image analysis and agricultural science), and Bayesian inference (including Markov chain Monte Carlo algorithms). Early life and education Besag was born in Loughborough and was educated at Loughborough Grammar School. He began studying engineering at the University of Cambridge but moved to the University of Birmingham to study statistics, obtaining his BSc in 1968. Career He then spent a year as a research assistant to Maurice Bartlett at the University of Oxford before obtaining a lectureship at the University of Liverpool. Inspired by John Tukey, he visited Princeton for a year. He moved to the University of Durham in 1975, where he became a professor in 1986. He was a visiting professor at the University of Washington in Seattle during 1989–90 and, after a year at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hammersley–Clifford Theorem
The Hammersley–Clifford theorem is a result in probability theory, mathematical statistics and statistical mechanics that gives necessary and sufficient conditions under which a strictly positive probability distribution can be represented as events generated by a Markov network (also known as a Markov random field). It is the fundamental theorem of random fields. It states that a probability distribution that has a strictly positive Probability mass function, mass or Probability density function, density satisfies one of the Markov random field#Definition, Markov properties with respect to an undirected graph ''G'' if and only if it is a Gibbs random field, that is, its density can be factorized over the cliques (or Complete graph, complete subgraphs) of the graph. The relationship between Markov and Gibbs random fields was initiated by Roland Dobrushin and Frank Spitzer in the context of statistical mechanics. The theorem is named after John Hammersley and Peter Clifford (statist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gibbs Sampling
In statistics, Gibbs sampling or a Gibbs sampler is a Markov chain Monte Carlo (MCMC) algorithm for sampling from a specified multivariate distribution, multivariate probability distribution when direct sampling from the joint distribution is difficult, but sampling from the Conditional probability distribution, conditional distribution is more practical. This sequence can be used to approximate the joint distribution (e.g., to generate a histogram of the distribution); to approximate the marginal distribution of one of the variables, or some subset of the variables (for example, the unknown parameters or latent variables); or to compute an integral (such as the expected value of one of the variables). Typically, some of the variables correspond to observations whose values are known, and hence do not need to be sampled. Gibbs sampling is commonly used as a means of statistical inference, especially Bayesian inference. It is a randomized algorithm (i.e. an algorithm that makes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edward Teller
Edward Teller (; January 15, 1908 – September 9, 2003) was a Hungarian and American Theoretical physics, theoretical physicist and chemical engineer who is known colloquially as "the father of the hydrogen bomb" and one of the creators of the History of the Teller–Ulam design, Teller–Ulam design based on Stanisław Ulam's design. He had a volatile personality, and was "driven by his megaton ambitions, had a Messiah complex, messianic complex, and displayed autocratic behavior." A thermonuclear design he devised was an Alarm Clock model bomb with a yield of 1000 MT (1 GT of TNT) and he proposed delivering it by boat or submarine. It would be capable of incinerating a continent. Born in Austria-Hungary in 1908, Teller emigrated to the US in the 1930s, one of the many so-called The Martians (scientists), "Martians", a group of Hungarian scientist émigrés. He made numerous contributions to Nuclear physics, nuclear and molecular physics, spectroscopy, and Surface science, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Augusta H
Augusta may refer to: Places Australia * Augusta, Western Australia Brazil * Rua Augusta (São Paulo) Canada * Augusta, Ontario * North Augusta, Ontario * Augusta Street (Hamilton, Ontario) France * Augusta Suessionum ("Augusta of the Suessii"), Soissons * Augusta Viromanduorum ("Augusta of the Viromandui"), Saint-Quentin Germany * Augusta Treverorum ("Augusta of the Treveri") or Trier * Augusta Vangionum ("Augusta of the Vangiones") or Worms * Augusta Vindelicorum ("Augusta of the Vindelici") or Augsburg Italy * Augusta, Sicily * Augusta Praetoria Salassorum ("Praetorian Augusta of the Salassi") or Aosta * Augusta Taurinorum ("Augusta of the Taurini") or Turin * Perugia or ''Augusta Perusia'' Spain * Emerita Augusta, Mérida, Spain * Caesar Augusta, Zaragoza, Spain United States * Augusta, Arkansas * Augusta Charter Township, Michigan * Augusta County, Virginia * Augusta, Georgia ** Augusta National Golf Club ("Augusta"), home of the Masters Tournament * Augusta, Il ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marshall Rosenbluth
Marshall Nicholas Rosenbluth (5 February 1927 – 28 September 2003) was an American plasma physicist and member of the National Academy of Sciences, and member of the American Philosophical Society. In 1997 he was awarded the National Medal of Science for discoveries in controlled thermonuclear fusion, contributions to plasma physics, and work in computational statistical mechanics. He was also a recipient of the E.O. Lawrence Prize (1964), the Albert Einstein Award (1967), the James Clerk Maxwell Prize for Plasma Physics (1976), the Enrico Fermi Award (1985), and the Hannes Alfvén Prize (2002). Early life and education Rosenbluth was born into a Jewish family and graduated from Stuyvesant High School in 1942. He did his undergraduate study at Harvard, graduating in 1946 (B.S., Phi Beta Kappa), while also serving in the U.S. Navy (1944–46). He received his Ph.D. in 1949 from the University of Chicago. Career During his first post-doctoral position at Stanford Univer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arianna W
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Arianna may refer to: * Ariana (name), a given name Opera * ''L'Arianna'', (English: ''Arianna''), by Monteverdi, first performed 1608 * ''Arianna'' (Marcello), by Benedetto Marcello, first concert performance 1727 * ''Arianna in Creta'', by Handel, first performed 1734 * ''Arianna'' (Goehr), by Alexander Goehr, first performed 1995 Other uses * ''Arianna'' (film), 2015 *ARIANNA Experiment, a proposed neutrino detector at the Ross Ice Shelf, Antarctica *Arianna (yacht), a 2012 luxury megayacht See also *Ariana (other) *Ariane (other) *Ariadne (other) *Aria (region), sometimes confused with Ariana *Aryana (TV series) ''Aryana'' is a Philippine television drama fantasy series broadcast by ABS-CBN. Directed by Erick C. Salud, Lino Cayetano, Lino S. Cayetano and Darnel Joy R. Villaflor. it stars Ella Cruz, Francis Magundayao, Paul Salas, Dominic Roque and Miche ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nicholas Metropolis
Nicholas Constantine Metropolis (Greek: ; June 11, 1915 – October 17, 1999) was a Greek-American physicist. Metropolis received his BSc (1937) and PhD in physics (1941, with Robert Mulliken) at the University of Chicago. Shortly afterwards, Robert Oppenheimer recruited him from Chicago, where he was collaborating with Enrico Fermi and Edward Teller on the first nuclear reactors, to the Los Alamos National Laboratory. He arrived in Los Alamos in April 1943, as a member of the original staff of fifty scientists. He came back to Los Alamos in 1948 to lead the group in the Theoretical Division that designed and built the MANIAC I computer in 1952 that was modeled on the IAS machine, and the MANIAC II in 1957. Early life and education Nicolas Metropolis was born on June 11, 1915, in Chicago, US. Metropolis received his BSc (1936) and PhD in chemical physics (1941) at the University of Chicago. During his PhD he worked with Robert Mulliken. After graduation, he worked as an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
