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Computational Statistics
Computational statistics, or statistical computing, is the study which is the intersection of statistics and computer science, and refers to the statistical methods that are enabled by using computational methods. It is the area of computational science (or scientific computing) specific to the mathematical science of statistics. This area is fast developing. The view that the broader concept of computing must be taught as part of general statistical education is gaining momentum. As in Statistics, traditional statistics the goal is to transform raw data into knowledge,Edward Wegman, Wegman, Edward J. �Computational Statistics: A New Agenda for Statistical Theory and Practice.�� Journal of the Washington Academy of Sciences', vol. 78, no. 4, 1988, pp. 310–322. ''JSTOR'' but the focus lies on computer intensive statistical methods, such as cases with very large Sample size determination, sample size and non-homogeneous data sets. The terms 'computational statistics' and 'statis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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London School Of Economics Statistics Machine Room 1964
London is the Capital city, capital and List of urban areas in the United Kingdom, largest city of both England and the United Kingdom, with a population of in . London metropolitan area, Its wider metropolitan area is the largest in Western Europe, with a population of 14.9 million. London stands on the River Thames in southeast England, at the head of a tidal estuary down to the North Sea, and has been a major settlement for nearly 2,000 years. Its ancient core and financial centre, the City of London, was founded by the Roman Empire, Romans as Londinium and has retained its medieval boundaries. The City of Westminster, to the west of the City of London, has been the centuries-long host of Government of the United Kingdom, the national government and Parliament of the United Kingdom, parliament. London grew rapidly 19th-century London, in the 19th century, becoming the world's List of largest cities throughout history, largest city at the time. Since the 19th cen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Monte Carlo Simulation
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle. The name comes from the Monte Carlo Casino in Monaco, where the primary developer of the method, mathematician Stanisław Ulam, was inspired by his uncle's gambling habits. Monte Carlo methods are mainly used in three distinct problem classes: optimization, numerical integration, and generating draws from a probability distribution. They can also be used to model phenomena with significant uncertainty in inputs, such as calculating the risk of a nuclear power plant failure. Monte Carlo methods are often implemented using computer simulations, and they can provide approximate solutions to problems that are otherwise intractable or too complex to analyze mathematically. Monte Carlo methods are widely used in various ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Random Number Book
A random number book is a book whose main content is a large number of random numbers or random digits. Such books were used in early cryptography and experimental design, and were published by the RAND Corporation and others. The RAND Corporation book ''A Million Random Digits with 100,000 Normal Deviates'' was first published in 1955 and was reissued in 2001. A sequel, ''A Million And One Random Digits'' was published in 2022. Tables of random numbers have probably been used for multiple purposes at least since the Industrial Revolution. A table of random numbers was made by L.H.C. Tippett. Random number books have been rendered obsolete for most purposes by the ready availability of random number generators running on electronic computers. However, they still have niche uses, particularly in the performance of experimental music pieces that call for them, such as ''Vision'' (1959) and ''Poem'' (1960) by La Monte Young. See also * One-time pad * Random number table Random n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Cumulative Distribution Function
In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x. Every probability distribution Support (measure theory), supported on the real numbers, discrete or "mixed" as well as Continuous variable, continuous, is uniquely identified by a right-continuous Monotonic function, monotone increasing function (a càdlàg function) F \colon \mathbb R \rightarrow [0,1] satisfying \lim_F(x)=0 and \lim_F(x)=1. In the case of a scalar continuous distribution, it gives the area under the probability density function from negative infinity to x. Cumulative distribution functions are also used to specify the distribution of multivariate random variables. Definition The cumulative distribution function of a real-valued random variable X is the function given by where the right-hand side represents the probability ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Pseudorandomness
A pseudorandom sequence of numbers is one that appears to be statistically random, despite having been produced by a completely deterministic and repeatable process. Pseudorandom number generators are often used in computer programming, as traditional sources of randomness available to humans (such as rolling dice) rely on physical processes not readily available to computer programs, although developments in hardware random number generator technology have challenged this. Background The generation of random numbers has many uses, such as for random sampling, Monte Carlo methods, board games, or gambling. In physics, however, most processes, such as gravitational acceleration, are deterministic, meaning that they always produce the same outcome from the same starting point. Some notable exceptions are radioactive decay and quantum measurement, which are both modeled as being truly random processes in the underlying physics. Since these processes are not practical sources of r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Biometrika
''Biometrika'' is a peer-reviewed scientific journal published by Oxford University Press for the Biometrika Trust. The editor-in-chief is Paul Fearnhead (Lancaster University). The principal focus of this journal is theoretical statistics. It was established in 1901 and originally appeared quarterly. It changed to three issues per year in 1977 but returned to quarterly publication in 1992. History ''Biometrika'' was established in 1901 by Francis Galton, Karl Pearson, and Raphael Weldon to promote the study of biometrics. The history of ''Biometrika'' is covered by Cox (2001). The name of the journal was chosen by Pearson, but Francis Edgeworth insisted that it be spelt with a "k" and not a "c". Since the 1930s, it has been a journal for statistical theory and methodology. Galton's role in the journal was essentially that of a patron and the journal was run by Pearson and Weldon and after Weldon's death in 1906 by Pearson alone until he died in 1936. In the early days, the Ameri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Student's T-distribution
In probability theory and statistics, Student's distribution (or simply the distribution) t_\nu is a continuous probability distribution that generalizes the Normal distribution#Standard normal distribution, standard normal distribution. Like the latter, it is symmetric around zero and bell-shaped. However, t_\nu has Heavy-tailed distribution, heavier tails, and the amount of probability mass in the tails is controlled by the parameter \nu. For \nu = 1 the Student's distribution t_\nu becomes the standard Cauchy distribution, which has very fat-tailed distribution, "fat" tails; whereas for \nu \to \infty it becomes the standard normal distribution \mathcal(0, 1), which has very "thin" tails. The name "Student" is a pseudonym used by William Sealy Gosset in his scientific paper publications during his work at the Guinness Brewery in Dublin, Ireland. The Student's distribution plays a role in a number of widely used statistical analyses, including Student's t- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Monte Carlo Method
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle. The name comes from the Monte Carlo Casino in Monaco, where the primary developer of the method, mathematician Stanisław Ulam, was inspired by his uncle's gambling habits. Monte Carlo methods are mainly used in three distinct problem classes: optimization, numerical integration, and generating draws from a probability distribution. They can also be used to model phenomena with significant uncertainty in inputs, such as calculating the risk of a nuclear power plant failure. Monte Carlo methods are often implemented using computer simulations, and they can provide approximate solutions to problems that are otherwise intractable or too complex to analyze mathematically. Monte Carlo methods are widely used in va ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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William Sealy Gosset
William Sealy Gosset (13 June 1876 – 16 October 1937) was an English statistician, chemist and brewer who worked for Guinness. In statistics, he pioneered small sample experimental design. Gosset published under the pen name Student and developed Student's t-distribution – originally called Student's "z" – and "Student's test of statistical significance". Life and career Born in Canterbury, England, Canterbury, England the eldest son of Agnes Sealy Vidal and Colonel Frederic Gosset, R.E. Royal Engineers, Gosset attended Winchester College before matriculating as Winchester Scholar in natural sciences and mathematics at New College, Oxford. Upon graduating in 1899, he joined the brewery of Arthur Guinness & Son in Dublin, Ireland; he spent the rest of his 38-year career at Guinness. The site cites ''Dictionary of Scientific Biography'' (New York: Scribner's, 1972), pp. 476–477; ''International Encyclopedia of Statistics'', vol. I (New York: Free Press, 1978), pp. 409–4 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Generalized Additive Model
In statistics, a generalized additive model (GAM) is a generalized linear model in which the linear response variable depends linearly on unknown smooth functions of some predictor variables, and interest focuses on inference about these smooth functions. GAMs were originally developed by Trevor Hastie and Robert Tibshirani to blend properties of generalized linear models with additive models. They can be interpreted as the discriminative generalization of the naive Bayes generative model. The model relates a univariate response variable, ''Y'', to some predictor variables, ''x''''i''. An exponential family distribution is specified for Y (for example normal, binomial or Poisson distributions) along with a link function ''g'' (for example the identity or log functions) relating the expected value of ''Y'' to the predictor variables via a structure such as : g(\operatorname(Y))=\beta_0 + f_1(x_1) + f_2(x_2)+ \cdots + f_m(x_m).\,\! The functions ''f''''i'' may be functions with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Artificial Neural Networks
In machine learning, a neural network (also artificial neural network or neural net, abbreviated ANN or NN) is a computational model inspired by the structure and functions of biological neural networks. A neural network consists of connected units or nodes called '' artificial neurons'', which loosely model the neurons in the brain. Artificial neuron models that mimic biological neurons more closely have also been recently investigated and shown to significantly improve performance. These are connected by ''edges'', which model the synapses in the brain. Each artificial neuron receives signals from connected neurons, then processes them and sends a signal to other connected neurons. The "signal" is a real number, and the output of each neuron is computed by some non-linear function of the sum of its inputs, called the '' activation function''. The strength of the signal at each connection is determined by a ''weight'', which adjusts during the learning process. Typically, neur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Kernel Density Estimation
In statistics, kernel density estimation (KDE) is the application of kernel smoothing for probability density estimation, i.e., a non-parametric method to estimate the probability density function of a random variable based on '' kernels'' as weights. KDE answers a fundamental data smoothing problem where inferences about the population are made based on a finite data sample. In some fields such as signal processing and econometrics it is also termed the Parzen–Rosenblatt window method, after Emanuel Parzen and Murray Rosenblatt, who are usually credited with independently creating it in its current form. One of the famous applications of kernel density estimation is in estimating the class-conditional marginal densities of data when using a naive Bayes classifier, which can improve its prediction accuracy. Definition Let be independent and identically distributed samples drawn from some univariate distribution with an unknown density at any given point . We are in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |