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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
Gibbs Mo dels 507
13.5.4 Validity of the model
The printout of a fitted model may indicate that it is ‘invalid’. By default, the canonical parameters
θ
are fitted without any constraint. However, most interpoint interactions have constraints on the
parameters. For example in the Strauss process, the interaction strength parameter
γ
must be less
than or equal to 1 in order to obtain a well-defined point process. Equivalently the canonical p a ram-
eter
θ
2
= log
γ
should be less tha n or equ a l to 0. This constraint is not imposed ( by default) by ppm
when it fits a Strauss model. Consider the redwood data , which are known to be very clustered:
> ppm(redwood
~
1, Strauss(0.1))
Stationary Strauss process
First order term: beta = 20.39
Interaction distance: 0.1
Fitted ...
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Publisher Resources

ISBN: 9781482210217