Covariance in probability theory and statistics is a measure of the joint variability of two random variables. The sign of the covariance, therefore,...

and statistics, a covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square...

Look up covariance or contravariance in Wiktionary, the free dictionary. Covariance and contravariance may refer to: Covariance and contravariance of...

average) or empirical mean (empirical average), and the sample covariance or empirical covariance are statistics computed from a sample of data on one or more...

through space". Lorentz covariance, a related concept, is a property of the underlying spacetime manifold. Lorentz covariance has two distinct, but closely...

together, and may refer to: Covariance matrix, a matrix of covariances between a number of variables Covariance or cross-covariance between two random variables...

In theoretical physics, general covariance, also known as diffeomorphism covariance or general invariance, consists of the invariance of the form of physical...

theory and statistics, the covariance function describes how much two random variables change together (their covariance) with varying spatial or temporal...

eigenvectors of the data's covariance matrix. Thus, the principal components are often computed by eigendecomposition of the data covariance matrix or singular...

statistics, sometimes the covariance matrix of a multivariate random variable is not known but has to be estimated. Estimation of covariance matrices then deals...

the covariance of two variables and the product of their standard deviations; thus, it is essentially a normalized measurement of the covariance, such...

" Regardless of Gaussianity, however, if the process and measurement covariances are known, then the Kalman filter is the best possible linear estimator...

In probability theory and statistics, the mathematical concepts of covariance and correlation are very similar. Both describe the degree to which two random...

Analysis of covariance (ANCOVA) is a general linear model that blends ANOVA and regression. ANCOVA evaluates whether the means of a dependent variable...

In statistics, the Matérn covariance, also called the Matérn kernel, is a covariance function used in spatial statistics, geostatistics, machine learning...

Covariance intersection (CI) is an algorithm for combining two or more estimates of state variables in a Kalman filter when the correlation between them...

Covariance matrix adaptation evolution strategy (CMA-ES) is a particular kind of strategy for numerical optimization. Evolution strategies (ES) are stochastic...

In physics, the principle of covariance emphasizes the formulation of physical laws using only those physical quantities the measurements of which the...

statistics and in probability theory, distance correlation or distance covariance is a measure of dependence between two paired random vectors of arbitrary...

probability theory and statistics, a cross-covariance matrix is a matrix whose element in the i, j position is the covariance between the i-th element of a random...

\operatorname {E} [X_{k}])^{\mathrm {T} },} and k × k {\displaystyle k\times k} covariance matrix Σ i , j = E ⁡ [ ( X i − μ i ) ( X j − μ j ) ] = Cov ⁡ [ X i , X...

a stochastic process, the autocovariance is a function that gives the covariance of the process with itself at pairs of time points. Autocovariance is...

function of the discrepancy between the observed covariance matrix and the model-implied covariance matrix. Chi-square increases with sample size only...

vectors in general are covariant since they can be pushed forward. See also Covariance and contravariance of vectors. Every functor F : C → D {\displaystyle...

well defined. Subtracting the mean before multiplication yields the auto-covariance function between times t 1 {\displaystyle t_{1}} and t 2 {\displaystyle...

{\displaystyle \left\{Y_{t}\right\}} , the cross-covariance is a function that gives the covariance of one process with the other at pairs of time points...

then we might choose a rougher covariance function. Extreme examples of the behaviour is the Ornstein–Uhlenbeck covariance function and the squared exponential...

Multivariate analysis of covariance (MANCOVA) is an extension of analysis of covariance (ANCOVA) methods to cover cases where there is more than one dependent...

In probability theory, the law of total covariance, covariance decomposition formula, or conditional covariance formula states that if X, Y, and Z are...

Gene–environment correlation (or genotype–environment correlation) is said to occur when exposure to environmental conditions depends on an individual's...