rDGS(beta, rho, W = owin(), expand=TRUE, nsim=1, drop=TRUE)"owin") in which to
generate the random pattern.
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.
nsim=1 and drop=TRUE (the default), the
result will be a point pattern, rather than a list
containing a point pattern.
nsim = 1, a point pattern (object of class "ppp").
If nsim > 1, a list of point patterns.
W
using a ‘perfect simulation’ algorithm.Diggle, Gates and Stibbard (1987) proposed a pairwise interaction point process in which each pair of points separated by a distance $d$ contributes a factor $e(d)$ to the probability density, where $$ e(d) = \sin^2\left(\frac{\pi d}{2\rho}\right) $$ for $d < rho$, and $e(d)$ is equal to 1 for $d >= rho$.
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.
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.
Diggle, P.J., Gates, D.J., and Stibbard, A. (1987) A nonparametric estimator for pairwise-interaction point processes. Biometrika 74, 763 -- 770. Scandinavian Journal of Statistics 21, 359--373.
Moller, J. and Waagepetersen, R. (2003). Statistical Inference and Simulation for Spatial Point Processes. Chapman and Hall/CRC.
rmh,
DiggleGatesStibbard. rStrauss,
rHardcore,
rStraussHard,
rDiggleGratton,
rPenttinen.