# rDGS

##### 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.

##### 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 $$ e(d) = \sin^2\left(\frac{\pi d}{2\rho}\right) $$ 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

If `nsim = 1`

, a point pattern (object of class `"ppp"`

).
If `nsim > 1`

, a list of point patterns.

##### 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

`rStrauss`

,
`rHardcore`

,
`rStraussHard`

,
`rDiggleGratton`

,
`rPenttinen`

.

##### Examples

```
# NOT RUN {
X <- rDGS(50, 0.05)
Z <- rDGS(50, 0.03, nsim=2)
# }
```

*Documentation reproduced from package spatstat, version 1.63-0, License: GPL (>= 2)*