Perfect Simulation of the Hardcore Process

Generate a random pattern of points, a simulated realisation of the Hardcore process, using a perfect simulation algorithm.

spatial, datagen
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.


Logical. If 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 W. Alternatively expand can be an object of class "rmhexpand" (see rmhexpand) determining the expansion method.


Number of simulated realisations to be generated.


Logical. If nsim=1 and 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 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 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.


If nsim = 1, a point pattern (object of class "ppp"). If 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.

See Also

rmh, Hardcore, rStrauss, rStraussHard, rDiggleGratton. rDGS, rPenttinen.

  • rHardcore
   X <- rHardcore(0.05,1.5,square(141.4))
   Z <- rHardcore(100,0.05, nsim=2)
# }
Documentation reproduced from package spatstat, version 1.64-1, License: GPL (>= 2)

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