Intrinsic Embedding Covariance Model
RMintrinsic is a univariate stationary isotropic covariance
model which depends on a univariate stationary isotropic covariance model.
The corresponding covariance function C of the model only depends on the distance r ≥ 0 between two points and is given by
C(r)=a_0 + a_2 r^2 + φ(r), 0≤ r ≤ diameter
C(r)=b_0 (rawR D - r)^3/(r), diameter ≤ r ≤ rawR * diameter
C(r) = 0, rawR * diameter ≤ r
RMintrinsic(phi, diameter, rawR, var, scale, Aniso, proj)
phi |
an |
diameter |
a numerical value; positive; should be the diameter of the domain on which simulation is done |
rawR |
a numerical value; greater or equal to 1 |
var,scale,Aniso,proj |
optional arguments; same meaning for any
|
The parameters a_0, a_2 and b_0
are chosen internally such that C becomes a smooth function.
See formulas (3.8)-(3.10) in Gneiting et alii (2006).
This model corresponds to the method Intrinsic Embedding.
See also RPintrinsic.
NOTE: The algorithm that checks the given parameters knows only about some few necessary conditions. Hence it is not ensured that the Stein-model is a valid covariance function for any choice of φ and the parameters.
For certain models phi, i.e. stable,
whittle, gencauchy, and the variogram
model fractalB some sufficient conditions are known.
RMintrinsic returns an object of class RMmodel.
Martin Schlather, schlather@math.uni-mannheim.de, https://www.wim.uni-mannheim.de/schlather/
Gneiting, T., Sevecikova, H, Percival, D.B., Schlather M., Jiang Y. (2006) Fast and Exact Simulation of Large Gaussian Lattice Systems in $R^2$: Exploring the Limits. J. Comput. Graph. Stat. 15, 483–501.
Stein, M.L. (2002) Fast and exact simulation of fractional Brownian surfaces. J. Comput. Graph. Statist. 11, 587–599
RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set ## RFoptions(seed=NA) to make them all random again x.max <- 10 model <- RMintrinsic(RMfbm(alpha=1), diameter=x.max) x <- seq(0, x.max, 0.02) plot(model) plot(RFsimulate(model, x=x))
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