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Semivariance
In spatial statistics the theoretical variogram 2\gamma(\mathbf_1,\mathbf_2) is a function describing the degree of spatial dependence of a spatial random field or stochastic process Z(\mathbf). The semivariogram \gamma(\mathbf_1,\mathbf_2) is half the variogram. In the case of a concrete example from the field of gold mining, a variogram will give a measure of how much two samples taken from the mining area will vary in gold percentage depending on the distance between those samples. Samples taken far apart will vary more than samples taken close to each other. Definition The semivariogram \gamma(h) was first defined by Matheron (1963) as half the average squared difference between the values at points (\mathbf_1 and \mathbf_2) separated at distance h. Formally :\gamma(h)=\frac\iiint_V \left (M+h) - f(M) \right2dV, where M is a point in the geometric field V, and f(M) is the value at that point. The triple integral is over 3 dimensions. h is the separation distance (e.g., ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variance
In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its population mean or sample mean. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value. Variance has a central role in statistics, where some ideas that use it include descriptive statistics, statistical inference, hypothesis testing, goodness of fit, and Monte Carlo sampling. Variance is an important tool in the sciences, where statistical analysis of data is common. The variance is the square of the standard deviation, the second central moment of a distribution, and the covariance of the random variable with itself, and it is often represented by \sigma^2, s^2, \operatorname(X), V(X), or \mathbb(X). An advantage of variance as a measure of dispersion is that it is more amenable to algebraic manipulation than other measures of dispersion such as the expected absolute deviatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variogram
In spatial statistics the theoretical variogram 2\gamma(\mathbf_1,\mathbf_2) is a function describing the degree of spatial dependence of a spatial random field or stochastic process Z(\mathbf). The semivariogram \gamma(\mathbf_1,\mathbf_2) is half the variogram. In the case of a concrete example from the field of gold mining, a variogram will give a measure of how much two samples taken from the mining area will vary in gold percentage depending on the distance between those samples. Samples taken far apart will vary more than samples taken close to each other. Definition The semivariogram \gamma(h) was first defined by Matheron (1963) as half the average squared difference between the values at points (\mathbf_1 and \mathbf_2) separated at distance h. Formally :\gamma(h)=\frac\iiint_V \left (M+h) - f(M) \right2dV, where M is a point in the geometric field V, and f(M) is the value at that point. The triple integral is over 3 dimensions. h is the separation distance (e.g., ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spatial Statistics
Spatial analysis or spatial statistics includes any of the formal techniques which studies entities using their topological, geometric, or geographic properties. Spatial analysis includes a variety of techniques, many still in their early development, using different analytic approaches and applied in fields as diverse as astronomy, with its studies of the placement of galaxies in the cosmos, to chip fabrication engineering, with its use of "place and route" algorithms to build complex wiring structures. In a more restricted sense, spatial analysis is the technique applied to structures at the human scale, most notably in the analysis of geographic data or transcriptomics data. Complex issues arise in spatial analysis, many of which are neither clearly defined nor completely resolved, but form the basis for current research. The most fundamental of these is the problem of defining the spatial location of the entities being studied. Classification of the techniques of spatial an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Positive Definite
In mathematics, positive definiteness is a property of any object to which a bilinear form or a sesquilinear form may be naturally associated, which is positive-definite. See, in particular: * Positive-definite bilinear form * Positive-definite function * Positive-definite function on a group * Positive-definite functional * Positive-definite kernel * Positive-definite matrix In mathematics, a symmetric matrix M with real entries is positive-definite if the real number z^\textsfMz is positive for every nonzero real column vector z, where z^\textsf is the transpose of More generally, a Hermitian matrix (that is, ... * Positive-definite quadratic form References *. *. {{Set index article, mathematics Quadratic forms ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geostatistics
Geostatistics is a branch of statistics focusing on spatial or spatiotemporal datasets. Developed originally to predict probability distributions of ore grades for mining operations, it is currently applied in diverse disciplines including petroleum geology, hydrogeology, hydrology, meteorology, oceanography, geochemistry, geometallurgy, geography, forestry, environmental control, landscape ecology, soil science, and agriculture (esp. in precision farming). Geostatistics is applied in varied branches of geography, particularly those involving the spread of diseases (epidemiology), the practice of commerce and military planning (logistics), and the development of efficient spatial networks. Geostatistical algorithms are incorporated in many places, including geographic information systems (GIS). Background Geostatistics is intimately related to interpolation methods, but extends far beyond simple interpolation problems. Geostatistical techniques rely on statistical models ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indicator Kriging
Indicator may refer to: Biology * Environmental indicator of environmental health (pressures, conditions and responses) * Ecological indicator of ecosystem health (ecological processes) * Health indicator, which is used to describe the health of a population * Honeyguides, also known as "indicator birds", a family of Old World tropical birds ** ''Indicator'' (genus), a genus of birds in the honeyguide family * Indicator species, a species that defines a characteristic of an environment * Indicator bacteria, bacteria used to detect and estimate the level of fecal contamination of water * Indicator organism, organisms used to measure such things as potential fecal contamination of environmental samples * Indicator plant, a plant that acts as a measure of environmental conditions * Indicator value, one of two terms in ecology referring to the classification of organisms * Iodine–starch test, a method to test for the presence of starch or iodine. Chemistry * Complexometric i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Outlier
In statistics, an outlier is a data point that differs significantly from other observations. An outlier may be due to a variability in the measurement, an indication of novel data, or it may be the result of experimental error; the latter are sometimes excluded from the data set. An outlier can be an indication of exciting possibility, but can also cause serious problems in statistical analyses. Outliers can occur by chance in any distribution, but they can indicate novel behaviour or structures in the data-set, measurement error, or that the population has a heavy-tailed distribution. In the case of measurement error, one wishes to discard them or use statistics that are robust to outliers, while in the case of heavy-tailed distributions, they indicate that the distribution has high skewness and that one should be very cautious in using tools or intuitions that assume a normal distribution. A frequent cause of outliers is a mixture of two distributions, which may be two dist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Resistant Statistics
Resistance may refer to: Arts, entertainment, and media Comics * Either of two similarly named but otherwise unrelated comic book series, both published by Wildstorm: ** ''Resistance'' (comics), based on the video game of the same title ** ''The Resistance'' (WildStorm), by Justin Gray, Jimmy Palmiotti, and Juan Santacruz * ''The Resistance'' (AWA Studios), an AWA Studios comic book meta series * ''Resistance: Book One'', graphic novel series by Carla Jablonski with art by Leland Purvis and published by First Second Books Fictional characters * Resistance (''Star Wars''), the primary protagonist organization in the Star Wars sequel trilogy *The Resistance, one of two factions in ''Ingress'' Films * ''Resistance'' (1945 film), a 1945 French film * ''Resistance'' (1992 film), a 1992 Australian film * ''Resistance'' (2003 film), a 2003 war film, with Bill Paxton * ''Resistance'' (2011 film), a 2011 war film, with Michael Sheen * ''Resistance'' (2020 film), a 2020 war film, with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Estimator
In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule (the estimator), the quantity of interest (the estimand) and its result (the estimate) are distinguished. For example, the sample mean is a commonly used estimator of the population mean. There are point and interval estimators. The point estimators yield single-valued results. This is in contrast to an interval estimator, where the result would be a range of plausible values. "Single value" does not necessarily mean "single number", but includes vector valued or function valued estimators. ''Estimation theory'' is concerned with the properties of estimators; that is, with defining properties that can be used to compare different estimators (different rules for creating estimates) for the same quantity, based on the same data. Such properties can be used to determine the best rules to use under given circumstances. However, in robust statistics, statistic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Square Root
In mathematics, a square root of a number is a number such that ; in other words, a number whose ''square'' (the result of multiplying the number by itself, or ⋅ ) is . For example, 4 and −4 are square roots of 16, because . Every nonnegative real number has a unique nonnegative square root, called the ''principal square root'', which is denoted by \sqrt, where the symbol \sqrt is called the '' radical sign'' or ''radix''. For example, to express the fact that the principal square root of 9 is 3, we write \sqrt = 3. The term (or number) whose square root is being considered is known as the ''radicand''. The radicand is the number or expression underneath the radical sign, in this case 9. For nonnegative , the principal square root can also be written in exponent notation, as . Every positive number has two square roots: \sqrt, which is positive, and -\sqrt, which is negative. The two roots can be written more concisely using the ± sign as \plusmn\sq ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Absolute Difference
The absolute difference of two real numbers x and y is given by , x-y, , the absolute value of their difference. It describes the distance on the real line between the points corresponding to x and y. It is a special case of the Lp distance for all 1\le p\le\infty and is the standard metric used for both the set of rational numbers \Q and their completion, the set of real numbers \R. As with any metric, the metric properties hold: * , x-y, \ge 0, since absolute value is always non-negative. * , x-y, = 0 if and only if x=y. * , x-y, =, y-x, ('' symmetry'' or '' commutativity''). * , x-z, \le, x-y, +, y-z, (''triangle inequality''); in the case of the absolute difference, equality holds if and only if x\le y\le z or x\ge y\ge z. By contrast, simple subtraction is not non-negative or commutative, but it does obey the second and fourth properties above, since x-y=0 if and only if x=y, and x-z=(x-y)+(y-z). The absolute diff ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
