RandomFields (version 3.0.32)

Coins: Random coin method

Description

The random coin method (or dilution method) is simulation method for stationary Gaussian random fields. It is based on the following procedure: For a stationary Poisson point process on ${\bf R}^d$ consider the random field $$Y(y) = \sum_{x\in X} f(y-x)$$ for a function $f$. The covariance of $Y$ is proportional to the convolution $$C(h) = \int f(x)f(x+h) dx$$ If the intensity of the Poisson point process increases, the random field $Y$ is approaches a Gaussian random field with covariance function $C$.

Usage

RPcoins(phi, shape, intensity) 
RPaverage(phi, shape, intensity)

Arguments

phi

object of class RMmodel; specifies the covariance function of the Poisson process; either phi or shape must be given.

shape

object of class RMmodel; specifies the function which is attached to the Poisson points; note that this is not the covariance function of the simulated random field.

intensity

positive number, intensity of the underlying Poisson point process.

Value

• RPcoins returns an object of class RMmodel

References

• Lantuejoul, C. (2002)Geostatistical Simulation: Models and Algorithms.Springer.

See Also

RFgetMethodNames RP, RPhyperplane, RPspectral, RPtbm.

Examples

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

\dontrun{
x <- seq(0,25, if (interactive()) 0.02 else 5)
model <- RPcoins(RMspheric())
z <- RFsimulate(model, x, x, spConform=FALSE) # takes 20 sec
Print(sd(as.vector(z)), mean(z))
image(z)


### Gaussian field approximates by Poisson fields
x <- seq(0,10, if (interactive()) 0.02 else 5)
for (intensity in c(1, 10, 100)) {
 z <- RFsimulate(x=x, model=RPcoins(RMspheric(), intensity = intensity))
 plot(z)
}
}

FinalizeExample()