Gibbs Mo dels 507
13.5.4 Validity of the model
The printout of a fitted model may indicate that it is ‘invalid’. By default, the canonical parameters
θ
are fitted without any constraint. However, most interpoint interactions have constraints on the
parameters. For example in the Strauss process, the interaction strength parameter
γ
must be less
than or equal to 1 in order to obtain a well-defined point process. Equivalently the canonical p a ram-
eter
θ
2
= log
γ
should be less tha n or equ a l to 0. This constraint is not imposed ( by default) by ppm
when it fits a Strauss model. Consider the redwood data , which are known to be very clustered:
> ppm(redwood
~
1, Strauss(0.1))
Stationary Strauss process
First order term: beta = 20.39
Interaction distance: 0.1
Fitted ...