# ragsAreaInter

##### Alternating Gibbs Sampler for Area-Interaction Process

Generate a realisation of the area-interaction process using the alternating Gibbs sampler. Applies only when the interaction parameter \(eta\) is greater than 1.

##### Usage

```
ragsAreaInter(beta, eta, r, …,
win = NULL, bmax = NULL, periodic = FALSE, ncycles = 100)
```

##### Arguments

- beta
First order trend. A number, a pixel image (object of class

`"im"`

), or a`function(x,y)`

.- eta
Interaction parameter (canonical form) as described in the help for

`AreaInter`

. A number greater than 1.- r
Disc radius in the model. A number greater than 1.

- …
Additional arguments for

`beta`

if it is a function.- win
Simulation window. An object of class

`"owin"`

. (Ignored if`beta`

is a pixel image.)- bmax
Optional. The maximum possible value of

`beta`

, or a number larger than this.- periodic
Logical value indicating whether to treat opposite sides of the simulation window as being the same, so that points close to one side may interact with points close to the opposite side. Feasible only when the window is a rectangle.

- ncycles
Number of cycles of the alternating Gibbs sampler to be performed.

##### Details

This function generates a simulated realisation of the
area-interaction process (see `AreaInter`

)
using the alternating Gibbs sampler (see `rags`

).

It exploits a mathematical relationship between the
(unmarked) area-interaction process and the two-type
hard core process (Baddeley and Van Lieshout, 1995;
Widom and Rowlinson, 1970). This relationship only holds
when the interaction parameter `eta`

is greater than 1
so that the area-interaction process is clustered.

The parameters `beta,eta`

are the canonical parameters described
in the help for `AreaInter`

.
The first order trend `beta`

may be a constant, a function,
or a pixel image.

The simulation window is determined by `beta`

if it is a pixel
image, and otherwise by the argument `win`

(the default is the
unit square).

##### Value

A point pattern (object of class `"ppp"`

).

##### References

Baddeley, A.J. and Van Lieshout, M.N.M. (1995).
Area-interaction point processes.
*Annals of the Institute of Statistical Mathematics*
**47** (1995) 601--619.

Widom, B. and Rowlinson, J.S. (1970).
New model for the study of liquid-vapor phase transitions.
*The Journal of Chemical Physics*
**52** (1970) 1670--1684.

##### See Also

##### Examples

```
# NOT RUN {
plot(ragsAreaInter(100, 2, 0.07, ncycles=15))
# }
```

*Documentation reproduced from package spatstat, version 1.57-1, License: GPL (>= 2)*