R: Non-Separable Space-Time model

RMnsst {RandomFields} | R Documentation

## Non-Separable Space-Time model

### Description

`RMnsst` is a univariate stationary spaceisotropic covariance model whose corresponding covariance is given by

C(h,u)= (ψ(u)+1)^{-δ/2} φ(h /√(ψ(u) +1))

### Usage

    RMnsst(phi, psi, delta, var, scale, Aniso, proj)

### Arguments

`phi` | is normal mixture `RMmodel`, cf. `RFgetModelNames(monotone="normal mixture")`
`psi` | is a variogram `RMmodel`.
`delta` | a numerical value; must be greater than or equal to the spatial dimension of the field
`var,scale,Aniso,proj` | optional arguments; same meaning for any `RMmodel`. If not passed, the above covariance function remains unmodified.

### Details

This model is used for space-time modelling where the spatial component is isotropic.

### Value

`RMnsst` returns an object of class `RMmodel`.

### Author(s)

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

### References

- Gneiting, T. (1997) Normal scale mixtures and dual probability densitites, J. Stat. Comput. Simul. 59, 375-384.

- Gneiting, T. (2002) Nonseparable, stationary covariance functions for space-time data, JASA 97, 590-600.

- Gneiting, T. and Schlather, M. (2001) Space-time covariance models. In El-Shaarawi, A.H. and Piegorsch, W.W.: The Encyclopedia of Environmetrics. Chichester: Wiley.

- Schlather, M. (2010) On some covariance models based on normal scale mixtures. Bernoulli, 16, 780-797.

### See Also

`RMgennsst`, `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

    model <- RMnsst(phi=RMgauss(), psi=RMfbm(alpha=1), delta=2)
    x <- seq(0, 10, 0.25)
    plot(model, dim=2)
    plot(RFsimulate(model, x=x, y=x))

[Package RandomFields version 3.1.50 Index]