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...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\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...

average value. It is the second central moment of a distribution, and the covariance of the random variable with itself, and it is often represented by σ 2...

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...

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

In physics, especially in multilinear algebra and tensor analysis, covariance and contravariance describe how the quantitative description of certain geometric...

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

{\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...

product ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot \rangle } , the covariance of P is the bilinear form Cov: H × H → R given by C o v ( x , y ) = ∫...

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

methodologies that seeks to represent hypotheses about the means, variances, and covariances of observed data in terms of a smaller number of 'structural' parameters...

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