Gaussian Covariance Model
RMgauss is a stationary isotropic covariance model.
The corresponding covariance function only depends on the distance
r ≥ 0 between two points and is given by
C(r)=e^{-r^2}.
RMgauss(var, scale, Aniso, proj)
var,scale,Aniso,proj |
optional arguments; same meaning for any
|
This model is called Gaussian because of the functional similarity of the spectral density of a process with that covariance function to the Gaussian probability density function.
The Gaussian model has an infinitely differentiable covariance function. This smoothness is artificial. Furthermore, this often leads to singular matrices and therefore numerically instable procedures (cf. Stein, M. L. (1999), p. 29).
The Gaussian model is included in the symmetric stable class (see
RMstable) for the choice alpha = 2.
The use of RMgauss is questionable from both a theoretical
(analytical paths) and a practical point of view (e.g. speed of
algorithms).
Instead, RMgneiting should be used.
Martin Schlather, schlather@math.uni-mannheim.de, https://www.wim.uni-mannheim.de/schlather/
Gelfand, A. E., Diggle, P., Fuentes, M. and Guttorp, P. (eds.) (2010) Handbook of Spatial Statistics. Boca Raton: Chapman & Hall/CRL.
Stein, M. L. (1999) Interpolation of Spatial Data. New York: Springer-Verlag
RMstable and RMmatern for generalizations;
RMmodel,
RFsimulate,
RFfit.
RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set ## RFoptions(seed=NA) to make them all random again model <- RMgauss(scale=0.4) x <- seq(0, 10, 0.02) plot(model) lines(RMgauss(), col="red") plot(RFsimulate(model, x=x))
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