# rStrauss

##### Perfect Simulation of the Strauss Process

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

##### Usage

`rStrauss(beta, gamma = 1, R = 0, W = owin())`

##### Arguments

- beta
- intensity parameter (a positive number).
- gamma
- interaction parameter (a number between 0 and 1, inclusive).
- R
- interaction radius (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
Strauss point process in the window `W`

using a

The Strauss process (Strauss, 1975; Kelly and Ripley, 1976)
is a model for spatial inhibition, ranging from
a strong `hard core' inhibition to a completely random pattern
according to the value of `gamma`

.

The Strauss process with interaction radius $R$ and parameters $\beta$ and $\gamma$ is the pairwise interaction point process with probability density $$f(x_1,\ldots,x_n) = \alpha \beta^{n(x)} \gamma^{s(x)}$$ where $x_1,\ldots,x_n$ represent the points of the pattern, $n(x)$ is the number of points in the pattern, $s(x)$ is the number of distinct unordered pairs of points that are closer than $R$ units apart, and $\alpha$ is the normalising constant. Intuitively, each point of the pattern contributes a factor $\beta$ to the probability density, and each pair of points closer than $r$ units apart contributes a factor $\gamma$ to the density.

The interaction parameter $\gamma$ must be less than or equal to $1$ in order that the process be well-defined (Kelly and Ripley, 1976). This model describes an ``ordered'' or ``inhibitive'' pattern. If $\gamma=1$ it reduces to a Poisson process (complete spatial randomness) with intensity $\beta$. If $\gamma=0$ it is called a ``hard core process'' with hard core radius $R/2$, since no pair of points is permitted to lie closer than $R$ units apart.

The simulation algorithm used to generate the point pattern
is `rmh`

, whose output
is only approximately correct).

The implementation is currently **experimental**.
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"`

).

##### 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.

Kelly, F.P. and Ripley, B.D. (1976)
On Strauss's model for clustering.
*Biometrika* **63**, 357--360.

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

Strauss, D.J. (1975)
A model for clustering.
*Biometrika* **63**, 467--475.

##### See Also

##### Examples

```
X <- rStrauss(0.05,0.2,1.5,square(141.4))
Z <- rStrauss(100,0.7,0.05)
```

*Documentation reproduced from package spatstat, version 1.10-2, License: GPL version 2 or newer*