
Cluster a nd Cox Models 479
7.752e-01 1.429e-08
Fitted mean of log of random intensity: 5.845
A cluster process with an average of 0.0678 points per cluster spread over a scale of 197 units, and
a Cox process with a tiny correlation rang e of 1.429e-08 units, are not physically meaningful.
This anomaly is caused by a quirk of th e pa rametrisation: the Poisson process does not corre-
spond to a p articular finite value of ψ. A Matérn cluster proc e ss in the unit square with huge cluster
radius is effectively a Poisson process. A log-Gaussian Cox process with tiny corr e la tion range is
also effectively a Poisson process. In theory, the Poisson pr