intensity.ppm.Rd
\name{intensity.ppm}
\alias{intensity.ppm}
\title{
Intensity of Fitted Point Process Model
}
\description{
Computes the intensity of a fitted point process model.
}
\usage{
\method{intensity}{ppm}(X, \dots)
}
\arguments{
\item{X}{
A fitted point process model (object of class \code{"ppm"}).
}
\item{\dots}{
Arguments passed to \code{\link{predict.ppm}} in some cases.
See Details.
}
}
\details{
This is a method for the generic function \code{\link{intensity}}
for fitted point process models (class \code{"ppm"}).
The intensity of a point process model is the expected
number of random points per unit area.
If \code{X} is a Poisson point process model, the intensity of the
process is computed exactly.
The result is a numerical value if \code{X}
is a stationary Poisson point process, and a pixel image if \code{X}
is non-stationary. (In the latter case, the resolution of the pixel
image is controlled by the arguments \code{\dots} which are passed
to \code{\link{predict.ppm}}.)
If \code{X} is another Gibbs point process model, the intensity is
computed approximately using the Poisson-saddlepoint approximation
(Baddeley and Nair, 2012a, 2012b, 2016; Anderssen et al, 2014).
The approximation is currently available for pairwise-interaction
models (Baddeley and Nair, 2012a, 2012b)
and for the area-interaction model and Geyer saturation model
(Baddeley and Nair, 2016).
For a non-stationary Gibbs model, the
pseudostationary solution (Baddeley and Nair, 2012b;
Anderssen et al, 2014) is used. The result is a pixel image,
whose resolution is controlled by the arguments \code{\dots} which are passed
to \code{\link{predict.ppm}}.
}
\value{
A numeric value (if the model is stationary)
or a pixel image.
}
\references{
Anderssen, R.S., Baddeley, A., DeHoog, F.R. and Nair, G.M. (2014)
Solution of an integral equation arising in spatial point process theory.
\emph{Journal of Integral Equations and Applications}
\bold{26} (4) 437--453.
Baddeley, A. and Nair, G. (2012a)
Fast approximation of the intensity of Gibbs point processes.
\emph{Electronic Journal of Statistics} \bold{6} 1155--1169.
Baddeley, A. and Nair, G. (2012b)
Approximating the moments of a spatial point process.
\emph{Stat} \bold{1}, 1, 18--30.
doi: 10.1002/sta4.5
Baddeley, A. and Nair, G. (2016)
Poisson-saddlepoint approximation for spatial point processes
with infinite order interaction.
Submitted for publication.
}
\seealso{
\code{\link{intensity}},
\code{\link{intensity.ppp}}
}
\examples{
fitP <- ppm(swedishpines ~ 1)
intensity(fitP)
fitS <- ppm(swedishpines ~ 1, Strauss(9))
intensity(fitS)
fitSx <- ppm(swedishpines ~ x, Strauss(9))
lamSx <- intensity(fitSx)
fitG <- ppm(swedishpines ~ 1, Geyer(9, 1))
lamG <- intensity(fitG)
fitA <- ppm(swedishpines ~ 1, AreaInter(7))
lamA <- intensity(fitA)
}
\author{
\adrian
and Gopalan Nair.
}
\keyword{spatial}
\keyword{models}