adaptive.density.Rd
\name{adaptive.density}
\alias{adaptive.density}
\title{Intensity Estimate of Point Pattern Using Tessellation}
\description{
Computes an adaptive estimate of the intensity function of a point
pattern.
}
\usage{
adaptive.density(X, f = 0.1, ..., nrep = 1)
}
\arguments{
\item{X}{Point pattern dataset (object of class \code{"ppp"}).}
\item{f}{Fraction (between 0 and 1) of the data points that will be
removed from the data and used to determine a tessellation for the
intensity estimate.
}
\item{\dots}{Arguments passed to \code{\link{as.im}} determining the
pixel resolution of the result.
}
\item{nrep}{Number of independent repetitions of the randomised procedure.}
}
\details{
This function is an alternative to \code{\link{density.ppp}}. It
computes an estimate of the intensity function of a point pattern
dataset.
The dataset \code{X} is randomly split into two patterns \code{A} and
\code{B} containing a fraction \code{f} and \code{1-f}, respectively,
of the original data. The subpattern \code{A} is used to construct a
Dirichlet tessellation (see \code{\link{dirichlet}}). The subpattern
\code{B} is retained for counting. For each tile of the Dirichlet
tessellation, we count the number of points of \code{B} falling in the
tile, and divide by the area of the same tile, to obtain an estimate
of the intensity of the pattern \code{B} in the tile.
This estimate is divided by \code{1-f} to obtain an estimate
of the intensity of \code{X} in the tile. The result is a pixel image
of intensity estimates which are constant on each tile of the tessellation.
If \code{nrep} is greater than 1, this randomised procedure is
repeated \code{nrep} times, and the results are averaged.
This technique has been used by Ogata et al. (2003), Ogata (2004)
and Baddeley (2007).
}
\value{
A pixel image (object of class \code{"im"}) whose values are
estimates of the intensity of \code{X}.
}
\seealso{
\code{\link{density.ppp}},
\code{\link{dirichlet}},
\code{\link{im.object}}.
}
\references{
Baddeley, A. (2007)
Validation of statistical models for spatial point patterns.
In J.G. Babu and E.D. Feigelson (eds.)
\emph{SCMA IV: Statistical Challenges in Modern Astronomy IV},
volume 317 of Astronomical Society of the Pacific Conference Series,
San Francisco, California USA, 2007. Pages 22--38.
Ogata, Y. (2004)
Space-time model for regional seismicity and detection of crustal
stress changes.
\emph{Journal of Geophysical Research}, \bold{109}, 2004.
Ogata, Y., Katsura, K. and Tanemura, M. (2003).
Modelling heterogeneous space-time occurrences of earthquake and its
residual analysis.
\emph{Applied Statistics} \bold{52} 499--509.
}
\examples{
\dontrun{
data(nztrees)
plot(adaptive.density(nztrees))
}
}
\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{methods}
\keyword{smooth}