rDGS {spatstat}R Documentation

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())

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((pi * d)/(2 * rho))

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.

Value

A point pattern (object of class "ppp").

Author(s)

Adrian Baddeley Adrian.Baddeley@csiro.au http://www.maths.uwa.edu.au/~adrian/ based on original code for the Strauss process by Kasper Klitgaard Berthelsen.

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, rDiggleGratton.

Examples

   X <- rDGS(50, 0.05)

[Package spatstat version 1.25-3 Index]