https://github.com/cran/spatstat
Revision d5016937b1541ef71363cfb819c876b827b3378a authored by Adrian Baddeley on 16 April 2009, 08:22:00 UTC, committed by cran-robot on 16 April 2009, 08:22:00 UTC
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Tip revision: d5016937b1541ef71363cfb819c876b827b3378a authored by Adrian Baddeley on 16 April 2009, 08:22:00 UTC
version 1.15-2
version 1.15-2
Tip revision: d501693
suffstat.Rd
\name{suffstat}
\alias{suffstat}
\title{Sufficient Statistic of Point Process Model}
\description{
The canonical sufficient statistic of a
point process model is evaluated for a given point pattern.
}
\usage{
suffstat(model, X=data.ppm(model))
}
\arguments{
\item{model}{A fitted point process model (object of class
\code{"ppm"}).
}
\item{X}{
A point pattern (object of class \code{"ppp"}).
}
}
\value{
A numeric vector of sufficient statistics. The entries
correspond to the model coefficients \code{coef(model)}.
}
\details{
The canonical sufficient statistic
of \code{model} is evaluated for the point pattern \code{X}.
This computation is useful for various Monte Carlo methods.
Here \code{model} should be a point process model (object of class
\code{"ppm"}, see \code{\link{ppm.object}}), typically obtained
from the model-fitting function \code{\link{ppm}}. The argument
\code{X} should be a point pattern (object of class \code{"ppp"}).
Every point process model fitted by \code{\link{ppm}} has
a probability density of the form
\deqn{f(x) = Z(\theta) \exp(\theta^T S(x))}{f(x) = Z(theta) exp(theta * S(x))}
where \eqn{x} denotes a typical realisation (i.e. a point pattern),
\eqn{\theta}{theta} is the vector of model coefficients,
\eqn{Z(\theta)}{Z(theta)} is a normalising constant,
and \eqn{S(x)} is a function of the realisation \eqn{x}, called the
``canonical sufficient statistic'' of the model.
For example, the stationary Poisson process has canonical sufficient
statistic \eqn{S(x)=n(x)}, the number of points in \eqn{x}.
The stationary Strauss process with interaction range \eqn{r}
(and no edge correction) has canonical sufficient statistic
\eqn{S(x)=(n(x),d(x))} where \eqn{d(x)} is the number of pairs
of points in \eqn{x} which are closer than a distance \eqn{r}
to each other.
\code{suffstat(model, X)} returns the value of \eqn{S(x)}, where \eqn{S} is
the canonical sufficient statistic associated with \code{model},
evaluated when \eqn{x} is the given point pattern \code{X}.
The result is a numeric vector, with entries which correspond to the
entries of the coefficient vector \code{coef(model)}.
The sufficient statistic \eqn{S}
does not depend on the fitted coefficients
of the model. However it does depend on the irregular parameters
which are fixed in the original call to \code{\link{ppm}}, for
example, the interaction range \code{r} of the Strauss process.
The sufficient statistic also depends on the edge correction that
was used to fit the model.
Non-finite values of the sufficient statistic (\code{NA} or
\code{-Inf}) may be returned if the point pattern \code{X} is
not a possible realisation of the model (i.e. if \code{X} has zero
probability of occurring under \code{model} for all values of
the canonical coefficients \eqn{\theta}{theta}).
}
\seealso{
\code{\link{ppm}}
}
\examples{
data(swedishpines)
fitS <- ppm(swedishpines, ~1, Strauss(7))
X <- rpoispp(summary(swedishpines)$intensity, win=swedishpines$window)
suffstat(fitS, X)
}
\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}
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