varcount.Rd
\name{varcount}
\alias{varcount}
\title{
Predicted Variance of the Number of Points
}
\description{
Given a fitted point process model, calculate the predicted variance
of the number of points in a nominated set \code{B}.
}
\usage{
varcount(model, B, \dots, dimyx = NULL)
}
\arguments{
\item{model}{
A fitted point process model
(object of class \code{"ppm"}, \code{"kppm"} or \code{"dppm"}).
}
\item{B}{
A window (object of class \code{"owin"} specifying the region in
which the points are counted.
Alternatively a pixel image (object of class \code{"im"})
or a function of spatial coordinates specifying a numerical weight
for each random point.
}
\item{\dots}{
Additional arguments passed to \code{B} when it is a function.
}
\item{dimyx}{
Spatial resolution for the calculations.
Argument passed to \code{\link{as.mask}}.
}
}
\details{
This command calculates the variance of the number of points
falling in a specified window \code{B} according to the \code{model}.
It can also calculate the variance of a sum of weights attached
to each random point.
The \code{model} should be a fitted point process model
(object of class \code{"ppm"}, \code{"kppm"} or \code{"dppm"}).
\itemize{
\item{
If \code{B} is a window, this command calculates the variance
of the number of points falling in \code{B}, according to the
fitted \code{model}.
If the \code{model} depends on spatial covariates other than the
Cartesian coordinates, then \code{B} should be a subset of the
domain in which these covariates are defined.
}
\item{
If \code{B} is a pixel image,
this command calculates the variance of
\eqn{T = \sum_i B(x_i)}{T = sum[i] B(x[i])},
the sum of the values of \code{B} over all random points
falling in the domain of the image.
If the \code{model} depends on spatial covariates other than the
Cartesian coordinates, then the domain of the pixel image,
\code{as.owin(B)}, should be a subset of the domain in which these
covariates are defined.
}
\item{
If \code{B} is a \code{function(x,y)} or \code{function(x,y,...)}
this command calculates the variance of
\eqn{T = \sum_i B(x_i)}{T = sum[i] B(x[i])},
the sum of the values of \code{B} over all random points
falling inside the window \code{W=as.owin(model)}, the window
in which the original data were observed.
}
}
The variance calculation involves the intensity and the
pair correlation function of the model.
The calculation is exact (up to discretisation error)
for models of class \code{"kppm"} and \code{"dppm"},
and for Poisson point process models of class \code{"ppm"}.
For Gibbs point process models of class \code{"ppm"} the
calculation depends on the Poisson-saddlepoint approximations
to the intensity and pair correlation function, which are rough
approximations. The approximation is not yet implemented
for some Gibbs models.
}
\value{
A single number.
}
\author{
\spatstatAuthors
}
\seealso{
\code{\link{predict.ppm}},
\code{\link{predict.kppm}},
\code{\link{predict.dppm}}
}
\examples{
fitT <- kppm(redwood ~ 1, "Thomas")
B <- owin(c(0, 0.5), c(-0.5, 0))
varcount(fitT, B)
fitS <- ppm(swedishpines ~ 1, Strauss(9))
BS <- square(50)
varcount(fitS, BS)
}
\keyword{spatial}
\keyword{models}