https://github.com/cran/RandomFields
Tip revision: e994a4415e67fa60cbfd3f208aaab20872521c0b authored by Martin Schlather on 14 February 2019, 21:02:19 UTC
version 3.3
version 3.3
Tip revision: e994a44
RPnugget.Rd
\name{Independent Variables}
\alias{RPnugget}
\alias{Nugget}
\title{Method to simulate the Nugget effect}
\description{
Method to simulate the Nugget effect. (Only for advanced users)
}
\usage{
RPnugget(phi, boxcox, tol, vdim)
}
\arguments{
\item{phi}{object of class \code{\link[=RMmodel-class]{RMmodel}};
specifies the covariance model to be simulated. The only possible
model for \code{phi} is \command{\link{RMnugget}}.}
\item{boxcox}{the one or two parameters of the box cox transformation.
If not given, the globally defined parameters are used.
See \command{\link{RFboxcox}} for details.
}
\item{tol}{
points at a distance less than or equal to \code{nugget.tol}
are considered as being identical. This strategy applies to
the simulation method and the covariance function itself.
Hence, the covariance function is only positive definite
if \code{nugget.tol=0.0}. However, if the anisotropy matrix
does not have full rank and \code{nugget.tol=0.0}, then
the simulations are likely to be odd.
The value of \code{nugget.tol}
should be of order \eqn{10^{-15}}{1e-15}.
Default: \code{0.0}
}
\item{vdim}{positive integer; the model is treated
\code{vdim}-variate, \code{vdim=1} (default) corresponds to a
univariate random field.
Mostly, the value of \code{vdim} is set automatically.
Default is that it takes the value of the submodel \code{phi}.}
}
\details{
\describe{
\item{General}{
This method only allows \command{\link{RMnugget}} as a submodel.
}
\item{Anisotropy}{
The method also allows for zonal nugget effects. Only there the
argument \code{tol} becomes important.
For the zonal nugget effect, the anisotropy matrix \code{Aniso}
should be given in \command{\link{RMnugget}}. There, only the
kernel of the
matrix is important.
}
\item{Points close together}{
The
locations at a distance less than or equal to the \link{RFoptions}
\code{nugget.tol}
are considered as being identical. This strategy applies to
the simulation method and the covariance function itself.
Hence, the covariance function is only positive definite
if \code{nugget.tol=0.0}. However, if the anisotropy matrix
does not have full rank and \code{nugget.tol=0.0}, then the
simulations are likely to be odd.
The value of \code{nugget.tol}
should be of order \eqn{10^{-15}}{1e-15}.
}
\item{Repeated measurements}{
Measurement errors are mathematically not distinguishable from spatial
nugget effects as long as measurements are not repeated at the very
same space-time
location. So there is no need to distinguish the spatial nugget
effect from a measurement error.
This is the default, see
\code{allow_duplicated_locations} in \link{RFoptions}.
In case several measurement have been taken in single space-time
locations,
measurement errors can be separated from spatial noise.
In this case \code{RMnugget()} models the measurement error (which
corresponds to a non-stationary model in an abstract space) by
default and the
measurement error model cannot be extended beyond the given
locations.
On the other hand \code{RMnugget(Ansio=something)} and
\code{RMnugget(proj=something)} model the spatial nugget effect
(with and without zonal anisotropy in case \code{Aniso} has low and
full rank respectively).
}
\item{Role of \command{RPnugget}}{
Even for advanced users, there is no need to call
\command{RPnugget} directly, as this is done internally when
the \link{RMnugget} is involved in the covariance model.
}
}
}
\value{
\code{RPnugget} returns an object of class
\code{\link[=RMmodel-class]{RMmodel}}.
}
\references{
\itemize{
\item
Schlather, M. (1999) \emph{An introduction to positive definite
functions and to unconditional simulation of random fields.}
Technical report ST 99-10, Dept. of Maths and Statistics,
Lancaster University.
}
}
\me
\seealso{ \link{Gaussian},
\link{RP},
\command{\link{RPcoins}},
\command{\link{RPhyperplane}},
\command{\link{RPspectral}},
\command{\link{RPtbm}}.
}
\keyword{methods}
\examples{\dontshow{StartExample()}
RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
## RFoptions(seed=NA) to make them all random again
x <- y <- 1:2
xy <- as.matrix(expand.grid(x, y)) ## we get 4 locations
## Standard use of the nugget effect
model <- RMnugget(var = 100)
RFcovmatrix(model, x=xy)
as.vector(RFsimulate(model, x=x, y=x, tol=1e-10))
## zonal nugget effect, which is not along the axes
model <- RMnugget(Aniso=matrix(1, nr=2, nc=2))
RFcovmatrix(model, x=xy)
as.vector(RFsimulate(model, x=x, y=x, tol=1e-10))
## All the following examples refer to repeated measurements
RFoptions(allow_duplicated_locations = TRUE)
(xy <- rbind(xy, xy)) ## now, the 4 locations are repeated twice
## standard situation: the nugget is interpreted as measurement error:
model <- RMnugget()
RFcovmatrix(model, x=xy)
as.matrix(RFsimulate(model, x=xy))
## any anisotropy matrix with full rank: spatial nugget effect
model <- RMnugget(Aniso=diag(2))
RFcovmatrix(model, x=xy)
as.matrix(RFsimulate(model, x=xy))
## anisotropy matrix with lower rank: zonal nugget effect
model <- RMnugget(Aniso=matrix(c(1, 0, 0, 0), nc=2))
RFcovmatrix(model, x=xy)
as.matrix(RFsimulate(model, x=xy))
## same as before: zonal nugget effect
model <- RMnugget(Aniso=t(c(1,0)))
RFcovmatrix(model, x=xy)
as.matrix(RFsimulate(model, x=xy))
\dontshow{FinalizeExample(); RFoptions(allow_duplicated_locations = FALSE) }}