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Parametric Estimation
Parametric statistics is a branch of statistics which leverages models based on a fixed (finite) set of parameters. Conversely nonparametric statistics does not assume explicit (finite-parametric) mathematical forms for distributions when modeling data. However, it may make some assumptions about that distribution, such as continuity or symmetry, or even an explicit mathematical shape but have a model for a distributional parameter that is not itself finite-parametric. Most well-known statistical methods are parametric. Regarding nonparametric (and semiparametric) models, Sir David Cox has said, "These typically involve fewer assumptions of structure and distributional form but usually contain strong assumptions about independencies". Example The normal family of distributions all have the same general shape and are ''parameterized'' by mean and standard deviation. That means that if the mean and standard deviation are known and if the distribution is normal, the probability ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Parameter
In statistics, as opposed to its general use in mathematics, a parameter is any quantity of a statistical population that summarizes or describes an aspect of the population, such as a mean or a standard deviation. If a population exactly follows a known and defined distribution, for example the normal distribution, then a small set of parameters can be measured which provide a comprehensive description of the population and can be considered to define a probability distribution for the purposes of extracting samples from this population. A "parameter" is to a population as a "statistic" is to a sample; that is to say, a parameter describes the true value calculated from the full population (such as the population mean), whereas a statistic is an estimated measurement of the parameter based on a sample (such as the sample mean, which is the mean of gathered data per sampling, called sample). Thus a "statistical parameter" can be more specifically referred to as a population ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ronald Fisher
Sir Ronald Aylmer Fisher (17 February 1890 – 29 July 1962) was a British polymath who was active as a mathematician, statistician, biologist, geneticist, and academic. For his work in statistics, he has been described as "a genius who almost single-handedly created the foundations for modern statistical science" and "the single most important figure in 20th century statistics". In genetics, Fisher was the one to most comprehensively combine the ideas of Gregor Mendel and Charles Darwin, as his work used mathematics to combine Mendelian genetics and natural selection; this contributed to the revival of Darwinism in the early 20th-century revision of the theory of evolution known as the Modern synthesis (20th century), modern synthesis. For his contributions to biology, Richard Dawkins declared Fisher to be the greatest of Darwin's successors. He is also considered one of the founding fathers of Neo-Darwinism. According to statistician Jeffrey T. Leek, Fisher is the most in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sufficient Statistic
In statistics, sufficiency is a property of a statistic computed on a sample dataset in relation to a parametric model of the dataset. A sufficient statistic contains all of the information that the dataset provides about the model parameters. It is closely related to the concepts of an ancillary statistic which contains no information about the model parameters, and of a complete statistic which only contains information about the parameters and no ancillary information. A related concept is that of linear sufficiency, which is weaker than ''sufficiency'' but can be applied in some cases where there is no sufficient statistic, although it is restricted to linear estimators. The Kolmogorov structure function deals with individual finite data; the related notion there is the algorithmic sufficient statistic. The concept is due to Sir Ronald Fisher in 1920. Stephen Stigler noted in 1973 that the concept of sufficiency had fallen out of favor in descriptive statistics because of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parametric Model
In statistics, a parametric model or parametric family or finite-dimensional model is a particular class of statistical models. Specifically, a parametric model is a family of probability distributions that has a finite number of parameters. Definition A statistical model is a collection of probability distributions on some sample space. We assume that the collection, , is indexed by some set . The set is called the parameter set or, more commonly, the parameter space. For each , let denote the corresponding member of the collection; so is a cumulative distribution function. Then a statistical model can be written as : \mathcal = \big\. The model is a parametric model if for some positive integer . When the model consists of absolutely continuous distributions, it is often specified in terms of corresponding probability density functions: : \mathcal = \big\. Examples * The Poisson family of distributions is parametrized by a single number : : ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inverse Problem
An inverse problem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating an image in X-ray computed tomography, sound source reconstruction, source reconstruction in acoustics, or calculating the density of the Earth from measurements of its gravity field. It is called an inverse problem because it starts with the effects and then calculates the causes. It is the inverse of a forward problem, which starts with the causes and then calculates the effects. Inverse problems are some of the most important mathematical problems in science and mathematics because they tell us about parameters that we cannot directly observe. They can be found in system identification, optics, radar, acoustics, communication theory, signal processing, medical imaging, computer vision, geophysics, oceanography, astronomy, remote sensing, natural language processing, machine learning, nondestructive testing, slope stability analys ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
All Models Are Wrong
"All models are wrong" is a common aphorism and anapodoton in statistics. It is often expanded as "All models are wrong, but some are useful". The aphorism acknowledges that statistical models always fall short of the complexities of reality but can still be useful nonetheless. The aphorism is generally attributed to George E. P. Box, a British statistician, although the underlying concept predates Box's writings. History The phrase "all models are wrong" was attributed to George Box who used the phrase in a 1976 paper to refer to the limitations of models, arguing that while no model is ever completely accurate, simpler models can still provide valuable insights if applied judiciously.. In their 1983 book on generalized linear models, Peter McCullagh and John Nelder stated that while modeling in science is a creative process, some models are better than others, even though none can claim eternal truth. In 1996, an Applied Statistician's Creed was proposed by M.R. Nester, which inc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aggregated Distribution
An aggregated distribution, commonly found among predators, parasites, and plants is a highly uneven (skewed) statistical distribution pattern in which they collect or aggregate in regions. These regions may be widely separated, particularly within animal distributions that are influenced by prey or host densities. This distribution makes sampling difficult and invalidates commonly-used parametric statistics. A similar pattern is found among predators that search for their prey. In predators When predators need to search for their prey, they could search at random, as has been assumed in models such as those made by Lotka in 1925 and Volterra in 1928. This would imply that they scatter themselves evenly across the environment. However, prey may be concentrated at high densities in some areas and scarce elsewhere. The zoologists M. P. Hassell and R. M. May noted that predators and parasites, too, might aggregate themselves where prey was abundant, choosing some response curve: they ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Methods For Research Workers
''Statistical Methods for Research Workers'' is a classic book on statistics, written by the statistician R. A. Fisher. It is considered by some to be one of the 20th century's most influential books on statistical methods, together with his '' The Design of Experiments'' (1935). It was originally published in 1925, by Oliver & Boyd (Edinburgh); the final and posthumous 14th edition was published in 1970. The impulse to write a book on the statistical methodology he had developed came not from Fisher himself but from D. Ward Cutler, one of the two editors of a series of "Biological Monographs and Manuals" being published by Oliver and Boyd. Reviews According to Denis Conniffe: Ronald A. Fisher was "interested in application and in the popularization of statistical methods and his early book ''Statistical Methods for Research Workers'', published in 1925, went through many editions and motivated and influenced the practical use of statistics in many fields of study. His ''Design ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-parametric Statistics
Nonparametric statistics is a type of statistical analysis that makes minimal assumptions about the underlying distribution of the data being studied. Often these models are infinite-dimensional, rather than finite dimensional, as in parametric statistics. Nonparametric statistics can be used for descriptive statistics or statistical inference. Nonparametric tests are often used when the assumptions of parametric tests are evidently violated. Definitions The term "nonparametric statistics" has been defined imprecisely in the following two ways, among others: The first meaning of ''nonparametric'' involves techniques that do not rely on data belonging to any particular parametric family of probability distributions. These include, among others: * Methods which are ''distribution-free'', which do not rely on assumptions that the data are drawn from a given parametric family of probability distributions. * Statistics defined to be a function on a sample, without dependency on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Wiley & Sons
John Wiley & Sons, Inc., commonly known as Wiley (), is an American Multinational corporation, multinational Publishing, publishing company that focuses on academic publishing and instructional materials. The company was founded in 1807 and produces books, Academic journal, journals, and encyclopedias, in print and electronically, as well as online products and services, training materials, and educational materials for undergraduate, graduate, and continuing education students. History The company was established in 1807 when Charles Wiley opened a print shop in Manhattan. The company was the publisher of 19th century American literary figures like James Fenimore Cooper, Washington Irving, Herman Melville, and Edgar Allan Poe, as well as of legal, religious, and other non-fiction titles. The firm took its current name in 1865. Wiley later shifted its focus to scientific, Technology, technical, and engineering subject areas, abandoning its literary interests. Wiley's son Joh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Independence (probability Theory)
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] |
Standard Deviation
In statistics, the standard deviation is a measure of the amount of variation of the values of a variable about its Expected value, mean. A low standard Deviation (statistics), deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range. The standard deviation is commonly used in the determination of what constitutes an outlier and what does not. Standard deviation may be abbreviated SD or std dev, and is most commonly represented in mathematical texts and equations by the lowercase Greek alphabet, Greek letter Sigma, σ (sigma), for the population standard deviation, or the Latin script, Latin letter ''s'', for the sample standard deviation. The standard deviation of a random variable, Sample (statistics), sample, statistical population, data set, or probability distribution is the square root of its variance. (For a finite population, v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
