spatstat (version 1.55-0)

rDGS: Perfect Simulation of the Diggle-Gates-Stibbard Process

Description

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

Usage

rDGS(beta, rho, W = owin(), expand=TRUE, nsim=1, drop=TRUE)

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.

expand

Logical. If 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

Number of simulated realisations to be generated.

drop

Logical. If nsim=1 and drop=TRUE (the default), the result will be a point pattern, rather than a list containing a point pattern.

Value

If nsim = 1, a point pattern (object of class "ppp"). If nsim > 1, a list of point patterns.

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.

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.

See Also

rmh, DiggleGatesStibbard.

rStrauss, rHardcore, rStraussHard, rDiggleGratton, rPenttinen.

Examples

# NOT RUN {
   X <- rDGS(50, 0.05)
# }