rStraussHard
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.
Usage
rStraussHard(beta, gamma = 1, R = 0, H = 0, W = owin(),
expand=TRUE, nsim=1, drop=TRUE)Arguments
- beta
intensity parameter (a positive number).
- gamma
interaction parameter (a number between 0 and 1, inclusive).
- R
interaction radius (a non-negative number).
- 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.- 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. Alternativelyexpandcan be an object of class"rmhexpand"(seermhexpand) determining the expansion method.- nsim
Number of simulated realisations to be generated.
- drop
Logical. If
nsim=1anddrop=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
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
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, 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
Examples
# NOT RUN {
Z <- rStraussHard(100,0.7,0.05,0.02)
Y <- rStraussHard(100,0.7,0.05,0.01, nsim=2)
# }