RandomFields (version 3.0.32)

RMnsst: Non-Separable Space-Time model

Description

RMnsst is a univariate stationary spaceisotropic covariance model whose corresponding covariance is given by $$C(h,u)= (\psi(u)+1)^{-\delta/2} \phi(h /\sqrt(\psi(u) +1))$$

Usage

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

Arguments

phi

is normal mixture RMmodel.

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.

Value

• RMnsst returns an object of class RMmodel.

Details

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

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,JASA97, 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.

  % \item Zastavnyi, V. and Porcu, E. (2011) % Caracterization theorems for the Gneiting class space-time % covariances. % \emph{Bernoulli}, \bold{??}.

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

See Also

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, if (interactive()) 0.2 else 1) 
plot(model, ylim=c(-1,1), dim=2)
plot(RFsimulate(model, x=x, y=x))
FinalizeExample()