Analysing spatial point patterns in R - CSIRO

22.2 Cox processes 141
22.2 Cox processes
A Cox point process is effectively a Poisson process with a random intensity function. Let Λ(u)
be a random function with non-negative values, defined at all locations u ∈ R 2 . Conditional on
Λ, let X be a Poisson process with intensity function Λ. Then X is a Cox process.
A trivial example is the “mixed Poisson” process in which we generate a random variable Λ
and, conditional on Λ, generate a uniform Poisson process with intensity Λ. Following are three
different realisations of this process:
> par(mfrow = c(1, 3))
> for (i in 1:3) {
+ lambda plot(rMaternI(70, 0.05))
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