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Taylor Diagram
Taylor diagrams are mathematical diagrams designed to graphically indicate which of several approximate representations (or models) of a system, process, or phenomenon is most realistic. This diagram, invented by Karl E. Taylor in 1994 (published in 2001) facilitates the comparative assessment of different models. It is used to quantify the degree of correspondence between the modeled and observed behavior in terms of three statistics: the Pearson correlation coefficient, the root-mean-square error (RMSE) error, and the standard deviation. Although Taylor diagrams have primarily been used to evaluate models designed to study climate and other aspects of Earth's environment, they can be used for purposes unrelated to environmental science (e.g., to quantify and visually display how well fusion energy models represent reality). Taylor diagrams can be constructed with a number of different open source and commercial software packages, including: GrADS, IDL, MATLAB, NCL, Python, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Diagram
Mathematical diagrams, such as charts and graphs, are mainly designed to convey mathematical relationships—for example, comparisons over time. Specific types of mathematical diagrams Argand diagram A complex number can be visually represented as a pair of numbers forming a vector on a diagram called an Argand diagram The complex plane is sometimes called the ''Argand plane'' because it is used in ''Argand diagrams''. These are named after Jean-Robert Argand (1768–1822), although they were first described by Norwegian-Danish land surveyor and mathematician Caspar Wessel (1745–1818). Argand diagrams are frequently used to plot the positions of the poles and zeroes of a function in the complex plane. The concept of the complex plane allows a geometric interpretation of complex numbers. Under addition, they add like vectors. The multiplication of two complex numbers can be expressed most easily in polar coordinates — the magnitude or ''modulus'' of the product is the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pearson Product-moment Correlation Coefficient
In statistics, the Pearson correlation coefficient (PCC, pronounced ) ― also known as Pearson's ''r'', the Pearson product-moment correlation coefficient (PPMCC), the bivariate correlation, or colloquially simply as the correlation coefficient ― is a measure of linear correlation between two sets of data. It is the ratio between the covariance of two variables and the product of their standard deviations; thus, it is essentially a normalized measurement of the covariance, such that the result always has a value between −1 and 1. As with covariance itself, the measure can only reflect a linear correlation of variables, and ignores many other types of relationships or correlations. As a simple example, one would expect the age and height of a sample of teenagers from a high school to have a Pearson correlation coefficient significantly greater than 0, but less than 1 (as 1 would represent an unrealistically perfect correlation). Naming and history It was developed by Ka ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Root Mean Square Deviation
The root-mean-square deviation (RMSD) or root-mean-square error (RMSE) is a frequently used measure of the differences between values (sample or population values) predicted by a model or an estimator and the values observed. The RMSD represents the square root of the second sample moment of the differences between predicted values and observed values or the quadratic mean of these differences. These deviations are called '' residuals'' when the calculations are performed over the data sample that was used for estimation and are called ''errors'' (or prediction errors) when computed out-of-sample. The RMSD serves to aggregate the magnitudes of the errors in predictions for various data points into a single measure of predictive power. RMSD is a measure of accuracy, to compare forecasting errors of different models for a particular dataset and not between datasets, as it is scale-dependent. RMSD is always non-negative, and a value of 0 (almost never achieved in practice) would i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standard Deviation
In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard 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. Standard deviation may be abbreviated SD, and is most commonly represented in mathematical texts and equations by the lower case Greek letter σ (sigma), for the population standard deviation, or the Latin letter '' s'', for the sample standard deviation. The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance. It is algebraically simpler, though in practice less robust, than the average absolute deviation. A useful property of the standard deviation is that, unlike the variance, it is expressed in the same unit as the data. The standard deviation of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physics Of Plasmas
''Physics of Plasmas'' is a peer-reviewed monthly scientific journal on plasma physics published by the American Institute of Physics, with cooperation by the American Physical Society The American Physical Society (APS) is a not-for-profit membership organization of professionals in physics and related disciplines, comprising nearly fifty divisions, sections, and other units. Its mission is the advancement and diffusion of k ...'s Division of Plasma Physics, since 1994. Until 1988, the journal topic was covered by '' Physics of Fluids''. From 1989 until 1993, ''Physics of Fluids'' was split into ''Physics of Fluids A'' covering fluid dynamics and ''Physics of Fluids B'' dedicated to plasma physics. In 1994, ''Physics of Plasmas'' was split off as a separate journal. External links * {{Official, http://pop.aip.org Monthly journals English-language journals American Institute of Physics academic journals Publications established in 1994 Plasma science journals ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Forecast Skill
In the fields of forecasting and prediction, forecast skill or prediction skill is any measure of the accuracy and/or degree of association of prediction to an observation or estimate of the actual value of what is being predicted (formally, the predictand); it may be quantified as a skill score. In meteorology, more specifically in weather forecasting, skill measures the superiority of a forecast over a simple historical baseline of past observations. The same forecast methodology can result in different skill scores at different places, or even in the same place for different seasons (e.g., spring weather might be driven by erratic local conditions, whereas winter cold snaps might correlate with observable polar winds). Weather forecast skill is often presented in the form of seasonal geographical maps. Forecast skill for single-value forecasts (i.e., time series of a scalar quantity) is commonly represented in terms of metrics such as correlation, root mean squared error, mea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Primer Fig1a
Primer may refer to: Arts, entertainment, and media Films * ''Primer'' (film), a 2004 feature film written and directed by Shane Carruth * ''Primer'' (video), a documentary about the funk band Living Colour Literature * Primer (textbook), a textbook used in primary education to teach the alphabet and other basic subjects * Primer (prayer book), a common name for English prayer books used from the 13th to 16th centuries * ''The New England Primer'' (1688), a Puritan book from Colonial America with morality-themed rhymes Music * ''Primer'' (album), a 1995 music album by the musical group Rockapella * Primer 55, an American alternative metal band * "The Primer", a song from the 2005 album ''Alaska'' by Between the Buried and Me Firearms * Primer (firearms), a firearm powder charge-ignition mechanism ** Centerfire ammunition, Boxer or Berdan primers used in modern centerfire cartridges ** Detonator, a small explosive device also known as an explosive primer or blasting cap ** ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Error Propagation
In statistics, propagation of uncertainty (or propagation of error) is the effect of variables' uncertainties (or errors, more specifically random errors) on the uncertainty of a function based on them. When the variables are the values of experimental measurements they have uncertainties due to measurement limitations (e.g., instrument precision) which propagate due to the combination of variables in the function. The uncertainty ''u'' can be expressed in a number of ways. It may be defined by the absolute error . Uncertainties can also be defined by the relative error , which is usually written as a percentage. Most commonly, the uncertainty on a quantity is quantified in terms of the standard deviation, , which is the positive square root of the variance. The value of a quantity and its error are then expressed as an interval . If the statistical probability distribution of the variable is known or can be assumed, it is possible to derive confidence limits to describe the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Law Of Cosines
In trigonometry, the law of cosines (also known as the cosine formula, cosine rule, or al-Kashi's theorem) relates the lengths of the sides of a triangle to the cosine of one of its angles. Using notation as in Fig. 1, the law of cosines states :c^2 = a^2 + b^2 - 2ab\cos\gamma, where denotes the angle contained between sides of lengths and and opposite the side of length . For the same figure, the other two relations are analogous: :a^2=b^2+c^2-2bc\cos\alpha, :b^2=a^2+c^2-2ac\cos\beta. The law of cosines generalizes the Pythagorean theorem, which holds only for right triangles: if the angle is a right angle (of measure 90 degrees, or radians), then , and thus the law of cosines reduces to the Pythagorean theorem: :c^2 = a^2 + b^2. The law of cosines is useful for computing the third side of a triangle when two sides and their enclosed angle are known. History Though the notion of the cosine was not yet developed in his time, Euclid's '' Elements'', dating back to th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taylor Diagram Fig2
Taylor, Taylors or Taylor's may refer to: People * Taylor (surname) ** List of people with surname Taylor * Taylor (given name), including Tayla and Taylah * Taylor sept, a branch of Scottish clan Cameron * Justice Taylor (other) Places Australia * Electoral district of Taylor, South Australia * Taylor, Australian Capital Territory, planned suburb Canada * Taylor, British Columbia United States * Taylor, Alabama * Taylor, Arizona * Taylor, Arkansas * Taylor, Indiana * Taylor, Louisiana * Taylor, Maryland * Taylor, Michigan * Taylor, Mississippi * Taylor, Missouri * Taylor, Nebraska * Taylor, North Dakota * Taylor, New York * Taylor, Beckham County, Oklahoma * Taylor, Cotton County, Oklahoma * Taylor, Pennsylvania * Taylors, South Carolina * Taylor, Texas * Taylor, Utah * Taylor, Washington * Taylor, West Virginia * Taylor, Wisconsin * Taylor, Wyoming * Taylor County (other) * Taylor Township (other) Businesses and organisations * Taylo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bias (statistics)
Statistical bias is a systematic tendency which causes differences between results and facts. The bias exists in numbers of the process of data analysis, including the source of the data, the estimator chosen, and the ways the data was analyzed. Bias may have a serious impact on results, for example, to investigate people's buying habits. If the sample size is not large enough, the results may not be representative of the buying habits of all the people. That is, there may be discrepancies between the survey results and the actual results. Therefore, understanding the source of statistical bias can help to assess whether the observed results are close to the real results. Bias can be differentiated from other mistakes such as accuracy (instrument failure/inadequacy), lack of data, or mistakes in transcription (typos). Bias implies that the data selection may have been skewed by the collection criteria. Bias does not preclude the existence of any other mistakes. One may have a poo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mean Error
In statistics and optimization, errors and residuals are two closely related and easily confused measures of the deviation of an observed value of an element of a statistical sample from its "true value" (not necessarily observable). The error of an observation is the deviation of the observed value from the true value of a quantity of interest (for example, a population mean). The residual is the difference between the observed value and the ''estimated'' value of the quantity of interest (for example, a sample mean). The distinction is most important in regression analysis, where the concepts are sometimes called the regression errors and regression residuals and where they lead to the concept of studentized residuals. In econometrics, "errors" are also called disturbances. Introduction Suppose there is a series of observations from a univariate distribution and we want to estimate the mean of that distribution (the so-called location model). In this case, the errors are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
