R: Gaussian Covariance Model

RMgauss {RandomFields} | R Documentation

## Gaussian Covariance Model

### Description

`RMgauss` is a stationary isotropic covariance model. The corresponding covariance function only depends on the distance r ≥ 0 between two points and is given by

C(r)=e^{-r^2}.

### Usage

    RMgauss(var, scale, Aniso, proj)

### Arguments

`var,scale,Aniso,proj` | optional arguments; same meaning for any `RMmodel`. If not passed, the above covariance function remains unmodified.

### Details

This model is called Gaussian because of the functional similarity of the spectral density of a process with that covariance function to the Gaussian probability density function.

The Gaussian model has an infinitely differentiable covariance function. This smoothness is artificial. Furthermore, this often leads to singular matrices and therefore numerically instable procedures (cf. Stein, M. L. (1999), p. 29).

The Gaussian model is included in the symmetric stable class (see `RMstable`) for the choice alpha = 2.

### Value

`RMgauss` returns an object of class `RMmodel`

### Note

The use of `RMgauss` is questionable from both a theoretical (analytical paths) and a practical point of view (e.g., speed of algorithms). Instead, `RMgneiting` should be used.

### Author(s)

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

### References

Gelfand, A. E., Diggle, P., Fuentes, M. and Guttorp, P. (eds.) (2010) Handbook of Spatial Statistics. Boca Raton: Chapman & Hall/CRL.

Stein, M. L. (1999) Interpolation of Spatial Data. New York: Springer-Verlag

### See Also

`RMstable` and `RMmatern` for generalisations;
`RMmodel`, `RFsimulate`, `RFfit`.

Do not mix up with `RPgauss` or `RRgauss`.

### Examples

    RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
    ##                   RFoptions(seed=NA) to make them all random again

    model <- RMgauss(scale=0.4)
    x <- seq(0, 10, 0.02)
    plot(model)
    lines(RMgauss(), col="red")
    plot(RFsimulate(model, x=x))

[Package RandomFields version 3.1.50 Index]