\name{Poisson}
\alias{Poisson}
\title{Poisson Point Process Model}
\description{
Creates an instance of the Poisson point process model
which can then be fitted to point pattern data.
}
\usage{
Poisson()
}
\value{
An object of class \code{"interact"}
describing the interpoint interaction
structure of the Poisson point process
(namely, there are no interactions).
}
\details{
The function \code{\link{ppm}}, which fits point process models to
point pattern data, requires an argument \code{interaction}
of class \code{"interact"}
describing the interpoint interaction structure
of the model to be fitted.
The appropriate description of the Poisson process is
provided by the value of the function \code{Poisson}.
This works for all types of Poisson processes including
multitype and nonstationary Poisson processes.
}
\seealso{
\code{\link{ppm}},
\code{\link{Strauss}},
\code{\link{StraussHard}}
}
\examples{
data(nztrees)
ppm(nztrees, ~1, Poisson())
# fit the stationary Poisson process to 'nztrees'
# no edge correction needed
data(longleaf)
\testonly{
longleaf <- longleaf[seq(1, longleaf$n, by=50)]
}
longadult <- longleaf[longleaf$marks >= 30, ]
longadult <- unmark(longadult)
ppm(longadult, ~ x, Poisson())
# fit the nonstationary Poisson process
# with intensity lambda(x,y) = exp( a + bx)
data(lansing)
# trees marked by species
\testonly{
lansing <- lansing[seq(1,lansing$n, by=30), ]
}
ppm(lansing, ~ marks, Poisson())
# fit stationary marked Poisson process
# with different intensity for each species
\dontrun{
ppm(lansing, ~ marks * polynom(x,y,3), Poisson())
}
# fit nonstationary marked Poisson process
# with different log-cubic trend for each species
\testonly{
# equivalent functionality - smaller dataset
data(betacells)
ppm(betacells, ~ marks * polynom(x,y,2), Poisson())
}
}
\author{Adrian Baddeley
\email{adrian@maths.uwa.edu.au}
\url{http://www.maths.uwa.edu.au/~adrian/}
and Rolf Turner
\email{r.turner@auckland.ac.nz}
}
\keyword{spatial}
\keyword{models}