RMnonstwm: Non-stationary Whittle-Matern Covariance Model

In RandomFields: Simulation and Analysis of Random Fields

Description

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

C(x, y)=Γ(μ) Γ(ν(x))^{-1/2} Γ(ν(y))^{-1/2} W_{μ} (|x-y|)

where μ = [ν(x) + ν(y)]/2, and ν must be a positive function.

W_{μ} 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.

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)

Example output

Loading required package: sp
Loading required package: RandomFieldsUtils

Attaching package: ‘RandomFields’

The following object is masked from ‘package:RandomFieldsUtils’:

    RFoptions

NOTE: simulation is performed with fixed random seed 0.
Set 'RFoptions(seed=NA)' to make the seed arbitrary.
....
New output format of RFsimulate: S4 object of class 'RFsp';
for a bare, but faster array format use 'RFoptions(spConform=FALSE)'.

RandomFields documentation built on Jan. 19, 2022, 1:06 a.m.