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Spatial Point Patterns
book

Spatial Point Patterns

by Adrian Baddeley, Ege Rubak, Rolf Turner
November 2015
Intermediate to advanced content levelIntermediate to advanced
828 pages
33h 11m
English
Chapman and Hall/CRC
Content preview from Spatial Point Patterns
344 Spatial Point Patterns: Methodology and Applications with R
9.7.4 Ma ximum likelihood for loglinear Poisson models
9.7.4.1 Loglinear models
For the vast majority of Poisson models treated in th is book, the intensity is a loglinear function of
the parameters:
λ
θ
(u) = exp(B(u) + θ
Z(u)) (9. 44)
where B(u) is a known function (the ‘offset’ or ‘log baseline’), θ = (
θ
1
,... ,
θ
p
) is the vector of
parameters, Z(u) = (Z
1
(u),... , Z
p
(u)) is a vector of covariate f unctions, and
θ
Z(u) =
θ
1
Z
1
(u) + ···+
θ
p
Z
p
(u).
Note that th e model implies that the logarithm of the intensity is a linear function of the parameters:
log
λ
θ
(u) = B(u) + θ
Z(u). (9.45)
The functions B and Z
1
,... ,Z
p
could be spa tially varyin g in any fashion, so this is a very wide and
flexible class ...
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Publisher Resources

ISBN: 9781482210217