416 Spatial Point Patterns: Methodology and Applications with R
49–50], [55]. Here w e present the simplest case, of residuals for a Poisson point process. Residuals
for Gibbs models are presented in Chapter 13.
A re sid ual is obtained by subtracting the fitted mean from the observed values. For a sp a tial point
process, the ‘mean’ is the intensity function , while the ‘ob served values’ are (naively spea king) the
data points of the point pattern. How can these be subtrac ted from each other?
For a fitted Poisson process model, w ith fitted intensity
b
λ
(u), the predicted number of points
falling in any region B is
R
B
b
λ
(u)du. The point process residual [55] for the region B is defined to
be the observed minus expected number of points falling in B:
R