# covariance function

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## covariance function

(koh-vair -ee-ăns) A statistical measure of the association of astronomical objects in a sample. See correlation function.
Collins Dictionary of Astronomy © Market House Books Ltd, 2006
References in periodicals archive ?
(iii) Let [x.sub.3,3] denote the quality of the covariance function used to model the network correlation errors.
Since the power variogram does not have a finite sill and integral scale and lacks an explicit form of covariance function, the SGSIM module in GSLIB does not have the support to use power variogram.
For each eigenfunction, a specific eigenvalue is associated as the first two eigenvalues for additive genetic and permanent environmental effects account for more than 98% of the total variation while the first three eigenvalues of the additive genetics and permanent covariance function accounted for at least 99.5% of the variations.
The fundamental information about the spectral quantity, that it must vanish at a lower and upper spectral limit, can be stated by the covariance function of a Brownian bridge process as described in Section 4.
On the other hand, Bohorquez (2010) conducted and analysis for predictive purposes the presence of PM10 in Bogota by using a non-separable covariance function, resulting in a predictive model of distribution space in the presence of PM10.
A Brownian stochastic flow {x(u, t), u [member of] R, t [greater than or equal to] 0} is called a Harris flow with covariance function r if for any u, v [member of] R the joint quadratic variation of the martingales {x(u, t), t [greater than or equal to] 0} and {x(v, t), t [greater than or equal to] 0} is given by
The elements of this matrix are determined with a suitable covariance function. Thus, the covariance functions of the signals are determined empirically with the help of the covariance functions.
The dependency can be specified via an arbitrary covariance function or kernel k([x.sub.p], [x.sub.q]).
A GP is completely specified by its mean function and covariance function. The mean function m(X) and the covariance function k(X,X') of a real process f(X) are defined as below:
The sample covariance function of f(x) = [[f.sub.1](x), [f.sub.2](x), ..., [f.sub.n](x)], x [member of] [[x.sub.1], [x.sub.p]] is given by
Assume that K(x) = K(x, [omega]) is a Gaussian log-normal field with known covariance function C(x, y).
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