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
. 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
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)
# }