
162 Spatial Point Patterns: Methodology and Applications with R
The left and m iddle panels of Figure 6.4 can be described by saying that the intensity value
λ
is spatially varying. At a spatial location u, the intensity is
λ
(u), wh ere
λ
(u) is some function of
location. More precisely, in a small neigh bourhood of the location u, with small area a, the expected
number of points is approximately equal to
λ
(u)a. For any region B, we may imagine dividing B
into pixels, ca lc ulating the expected number of points in each pixel, and adding up these expected
numbers to obtain the expected total number of points in B. This sum is effectively the integral