R: Perfect Simulation of the Strauss-Hardcore Process

rStraussHard {spatstat.random} | R Documentation

## Perfect Simulation of the Strauss-Hardcore Process

### Description

Generate a random pattern of points, a simulated realisation of the Strauss-Hardcore process, using a perfect simulation algorithm.

### Usage

      rStraussHard(beta, gamma = 1, R = 0, H = 0, W = owin(),
                   expand=TRUE, nsim=1, drop=TRUE)

### Arguments

`beta` | intensity parameter (a positive number).
`gamma` | interaction parameter (a number between 0 and 1, inclusive).
`R` | interaction radius (a non-negative number).
`H` | hard core distance (a non-negative number smaller than `R`).
`W` | window (object of class `"owin"`) in which to generate the random pattern. Currently this must be a rectangular window.
`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 Strauss-Hardcore point process in the window `W` using a ‘perfect simulation’ algorithm.

The Strauss-Hardcore process is described in `StraussHard`.

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).

A limitation of the perfect simulation algorithm is that the interaction parameter gamma must be less than or equal to 1. To simulate a Strauss-hardcore process with gamma > 1, use `rmh`.

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)

Kasper Klitgaard Berthelsen and Adrian Baddeley Adrian.Baddeley@curtin.edu.au

### 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.

Moller, J. and Waagepetersen, R. (2003). Statistical Inference and Simulation for Spatial Point Processes. Chapman and Hall/CRC.

### See Also

`rmh`, `StraussHard`.

`rHardcore`, `rStrauss`, `rDiggleGratton`, `rDGS`, `rPenttinen`.

### Examples

       Z <- rStraussHard(100,0.7,0.05,0.02)
       Y <- rStraussHard(100,0.7,0.05,0.01, nsim=2)

[Package spatstat.random version 2.1-0 Index]