rHardcore
Perfect Simulation of the Hardcore Process
Generate a random pattern of points, a simulated realisation of the Hardcore process, using a perfect simulation algorithm.
Usage
rHardcore(beta, R = 0, W = owin(), expand=TRUE, nsim=1, drop=TRUE)
Arguments
 beta
 intensity parameter (a positive number).
 R
 hard core distance (a nonnegative number).
 W

window (object of class
"owin"
) in which to generate the random pattern. Currently this must be a rectangular window.  expand

Logical. If
FALSE
, simulation is performed in the windowW
, which must be rectangular. IfTRUE
(the default), simulation is performed on a larger window, and the result is clipped to the original windowW
. Alternativelyexpand
can be an object of class"rmhexpand"
(seermhexpand
) determining the expansion method.  nsim
 Number of simulated realisations to be generated.
 drop

Logical. If
nsim=1
anddrop=TRUE
(the default), the result will be a point pattern, rather than a list containing a point pattern.
Details
This function generates a realisation of the
Hardcore point process in the window W
using a ‘perfect simulation’ algorithm.
The Hardcore process is a model for strong spatial inhibition.
Two points of the process are forbidden to lie closer than
R
units apart.
The Hardcore process is the special case of the Strauss process
(see rStrauss
)
with interaction parameter $gamma$ equal to zero.
The simulation algorithm used to generate the point pattern
is ‘dominated coupling from the past’
as implemented by Berthelsen and Moller (2002, 2003).
This is a ‘perfect simulation’ or ‘exact simulation’
algorithm, so called because the output of the algorithm is guaranteed
to have the correct probability distribution exactly (unlike the
MetropolisHastings algorithm used in rmh
, whose output
is only approximately correct).
There is a tiny chance that the algorithm will run out of space before it has terminated. If this occurs, an error message will be generated.
Value

If
nsim = 1
, a point pattern (object of class "ppp"
).
If nsim > 1
, a list of point patterns.
References
Berthelsen, K.K. and Moller, J. (2002) A primer on perfect simulation for spatial point processes. Bulletin of the Brazilian Mathematical Society 33, 351367.
Berthelsen, K.K. and Moller, J. (2003) Likelihood and nonparametric Bayesian MCMC inference for spatial point processes based on perfect simulation and path sampling. Scandinavian Journal of Statistics 30, 549564.
Moller, J. and Waagepetersen, R. (2003). Statistical Inference and Simulation for Spatial Point Processes. Chapman and Hall/CRC.
See Also
rmh
,
Hardcore
,
rStrauss
,
rStraussHard
,
rDiggleGratton
.
rDGS
,
rPenttinen
.
Examples
X < rHardcore(0.05,1.5,square(141.4))
Z < rHardcore(100,0.05)