# Generating pattern of points from a pairwise interaction space point process

I have estimated the parameters of a non-homogeneous poisson space point process using Metropolis+gibbs from some observation data. I know:

$N$: Number of points inside my observation window

$\lambda$: Intensity function

and the parameters associated with this intensity function.

If I want to generate a pattern of points using the intensity function $\lambda$. This is possible with the function rpoint from the r library spatstat: https://stackoverflow.com/questions/33874879/how-to-generate-spatial-points-with-a-pattern

My question is how in general can I generate patterns of points for any distribution function assuming that I have done inference about the parameters already. I know that rpoint assumes independence between points but how can I generate a pattern of m points from a different point process, let's say the Area interaction point process assuming that I have estimated the parameters? I have read some about the reject sampling but is not straightforward to me how to do this.

By the way, the same r package has a function that brings a pattern of points for the area-interaction process but I can not specify the $m$ number of points to be generated.

Thanks

## 1 Answer

I only have my phone here so my answer will be a bit rough around the edges. I believe you are looking for the function rmh.default in spatstat. To do simulation conditionally on the number of points you can set the control parameter p to 1 as described in the help file. The second example of the help file shows how to simulate a Strauss process with the number of points fixed to 42.