Perfect Simulation of the Hardcore Process
Generate a random pattern of points, a simulated realisation of the Hardcore process, using a perfect simulation algorithm.
rHardcore(beta, R = 0, W = owin(), expand=TRUE, nsim=1, drop=TRUE)
- intensity parameter (a positive number).
- hard core distance (a non-negative number).
window (object of class
"owin") in which to generate the random pattern. Currently this must be a rectangular window.
FALSE, simulation is performed in the window
W, which must be rectangular. If
TRUE(the default), simulation is performed on a larger window, and the result is clipped to the original window
expandcan be an object of class
rmhexpand) determining the expansion method.
- Number of simulated realisations to be generated.
drop=TRUE(the default), the result will be a point pattern, rather than a list containing a point pattern.
This function generates a realisation of the
Hardcore point process in the window
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
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
Metropolis-Hastings 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.
nsim = 1, a point pattern (object of class
nsim > 1, a list of point patterns.
Berthelsen, K.K. and Moller, J. (2002) A primer on perfect simulation for spatial point processes. Bulletin of the Brazilian Mathematical Society 33, 351-367.
Berthelsen, K.K. and Moller, J. (2003) Likelihood and non-parametric Bayesian MCMC inference for spatial point processes based on perfect simulation and path sampling. Scandinavian Journal of Statistics 30, 549-564.
Moller, J. and Waagepetersen, R. (2003). Statistical Inference and Simulation for Spatial Point Processes. Chapman and Hall/CRC.
X <- rHardcore(0.05,1.5,square(141.4)) Z <- rHardcore(100,0.05)