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

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(), 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.

### 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

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

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au, 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`, `rStraussHard`, `rDiggleGratton`, `rPenttinen`.

### Examples

       X <- rDGS(50, 0.05)

[Package spatstat version 1.54-0 Index]