
492 Spatial Point Patterns: Methodology and Applications with R
Take the probability density of CSR, eq uation (13.1), and modif y it b y requiring that f (x) = 0 if the
pattern violates the hard core c ondition. The new model has the probability density
f (x) =
c
2
β
n(x)
if hard core is satisfied
0 if hard core is violated
(13.3)
where c
2
is another constant (which is difficult to calculate). This is the probability density of the
Gibbs ha rd core process, usually just called ‘the’ hard core process. On e way to interpret this model
is that
‘the hard core process is the Po isson proce ss conditional on the event that it satisfies the hard
core constraint.