RMnonstwm {RandomFields}

R Documentation

Non-stationary Whittle-Matern Covariance Model

Description

The non-stationary Whittle-Matern model C is given by

C(x, y)=\Gamma(\mu) \Gamma(\nu(x))^{-1/2} \Gamma(\nu(y))^{-1/2} W_{\mu} (|x-y|)

where \mu = [\nu(x) + \nu(y)]/2, and \nu must be a positive function.

W_{\mu} is the covariance of the RMwhittle model or the RMmatern model.

Details

The non-stationary Whittle-Matern models are obtained by the respective stationary model, replacing the real-valued argument for nu by a non-negative function.

Note

It cannot be checked whether nu only takes positive values. So the responsibility is completely left to the user.

Author(s)

Martin Schlather, schlather@math.uni-mannheim.de, https://www.wim.uni-mannheim.de/schlather/

References

• Stein, M. (2005) Nonstationary Spatial Covariance Functions. Tech. Rep., 2005

See Also

RMwhittle, RMmodel, RFsimulate, RFfit.

Examples

RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
##                   RFoptions(seed=NA) to make them all random again
x <- seq(-1.2, 1.2, len=50)
model <- RMwhittle(nu=RMgauss())

z <- RFsimulate(model=model, x, x, n=4)
plot(z)

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