304 Spatial Point Patterns: Methodology and Applications with R
the m odel. Then the overall process is an in homogeneo us Poisson process where the intensity
function
λ
(u) takes the value
β
j
when u is in region B
j
. See Figure 9 .2.
intensity proportional to baseline: A simp le model is
λ
(u) =
θ
b(u) (9.3)
where b(u) is a known function (‘baseline’) and
θ
is an unknown param eter that must be es-
timated. If the baseline b(u) repr e sents the spatially varying density of a population, and we
assume th at each member of th e population has equal cha nce
θ
of c ontracting a rare disease, then
the cases of the disease will form a Poisson process with intensity (9.3), the ‘co nstant risk’ model.
Modelling scenarios which involve rand om thinning often lead to