512 Spatial Point Patterns: Methodology and Applications with R
Simulation also makes possible a wide variety of techniques for validatin g the model. At a
simple level we can assess whether the simulated patterns produce roug hly th e same number of
points as the data:
> npoints(swedishpines)
[1] 71
> np <- sapply(s, npoints)
> mean(np)
[1] 71.58
> sd(np)
[1] 6.703
However, ‘validation’ of this kind can g ive a false sense of security. For a Poisson point process
model, under typical conditions, the expected total number of points generated by the fitted model
must be equal to the observed number of points. (This is implied by the score equations, if th e
model includes an intercept term and has been fitted by maximum likelihoo d.) For a Gibbs process,