# rStraussHard

0th

Percentile

##### Perfect Simulation of the Strauss-Hardcore Process

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

Keywords
spatial, datagen
##### Usage
rStraussHard(beta, gamma = 1, R = 0, H = 0, W = owin())
##### Arguments
beta
intensity parameter (a positive number).
gamma
interaction parameter (a number between 0 and 1, inclusive).
R
H
hard core distance (a non-negative number smaller than R).
W
window (object of class "owin") in which to generate the random pattern. Currently this must be a rectangular window.
##### Details

This function generates a realisation of the Strauss-Hardcore point process in the window W using a perfect simulation algorithm.

The Strauss-Hardcore process is described in StraussHard.

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).

A limitation of the perfect simulation algorithm is that the interaction parameter $\gamma$ must be less than or equal to $1$. To simulate a Strauss-hardcore process with $\gamma > 1$, use rmh.

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

• A point pattern (object of class "ppp").

##### References

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.

rmh, rStrauss, StraussHard.
Z <- rStraussHard(100,0.7,0.05,0.02)