R: Intrinsic Embedding Covariance Model

RMintrinsic {RandomFields} | R Documentation

## 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 ≥ 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

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

### 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 φ and the parameters.

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

### Value

`RMintrinsic` returns an object of class `RMmodel`

### Author(s)

Martin Schlather, schlather@math.uni-mannheim.de

### References

- 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

### See Also

`RPintrinsic`, `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.max <- 10
    model <- RMintrinsic(RMfbm(alpha=1), diameter=x.max)
    x <- seq(0, x.max, 0.02)
    plot(model)
    plot(RFsimulate(model, x=x))

[Package RandomFields version 3.1.50 Index]