RandomFields (version 3.0.5)

RMintrinsic: Intrinsic Embedding Covariance Model

Description

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 $r \ge 0$ between two points and is given by $$C(r)=a_0 + a_2 r^2 + \phi(r), 0\le r \le diameter$$ $$C(r)=b_0 (rawR D - r)^3/(r), diameter \le r \le rawR * diameter$$ $$C(r) = 0, rawR * diameter \le r$$

Usage

RMintrinsic(phi, diameter, rawR, var, scale, Aniso, proj)

Arguments

phi

an RMmodel; has to be stationary and isotropic

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 parameters; same meaning for any RMmodel. If not passed, the above covariance function remains unmodified.

Value

• RMintrinsic returns an object of class RMmodel

Details

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 phi and the parameters. For certain models $\phi$, i.e. stable, whittle, gencauchy, and the variogram model fractalB some sufficient conditions are known.

References

• Gneiting, T., Sevecikova, H, Percival, D.B., Schlather M., Jiang Y. (2006) Fast and Exact Simulation of Large {G}aussian 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

See Also

RPintrinsic, RMmodel, RFsimulate, RFfit.

Examples

set.seed(0)
x.max <- 10
model <- RMintrinsic(RMfbm(alpha=1), diameter=x.max)
x <- seq(0, x.max, if (interactive()) 0.02 else 1) 
plot(model, ylim=c(0,6))
plot(RFsimulate(model, x=x))