
474 Spatial Point Patterns: Methodology and Applications with R
For a log-Gaussian Cox process, we need to remember that
λ
(u) = EΛ(u) = E exp(G(u)) is equal
to e
µ
(u)+
σ
2
/2
, where
µ
(u) is n ow th e mean function of the Gaussian random field an d
σ
2
= C(0) is
its variance. Therefore th e mean function of the Gaussian random field is not log
λ
(u) but
µ
(u) = −
σ
2
2
+ B(u) +
θ
⊤
Z(u). (12.16)
Notice the absence of log on the left side.
Note that inhomogeneous models of this kind are ‘correlation-stationary’ as defined in Sec-
tion 7.10.2. The f ormal test for correlation -stationarity describe d in Section 16.8.5 could be used to
decide whe ther such models are appropriate ...