# rDGS

0th

Percentile

##### Perfect Simulation of the Diggle-Gates-Stibbard Process

Generate a random pattern of points, a simulated realisation of the Diggle-Gates-Stibbard process, using a perfect simulation algorithm.

Keywords
spatial, datagen
##### Usage
rDGS(beta, rho, W = owin())
##### Arguments
beta
intensity parameter (a positive number).
rho
interaction range (a non-negative number).
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 Diggle-Gates-Stibbard point process in the window 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 $d \ge \rho$.

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.

##### 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.

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, rDiggleGratton.
X <- rDGS(50, 0.05)