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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 557
That is, the indicator s I
i
satisfy a conditional autologistic regression. The model can be fitted by
maximising the logistic composite log-likelihoo d
LRL(θ) =
x
i
x
log
λ
θ
(x
i
| x)
δ
(x
i
) +
λ
θ
(x
i
| x)
+
d
j
d
log
δ
(d
j
)
δ
(d
j
) +
λ
θ
(d
j
| x)
(13.84)
which is Besag’s discrete log-pseudolikelihood for the indicators (I
i
) given the locations y. This can
be maximised using standard software for logistic regression. The loglikeliho od is a concave func-
tion of θ, and conditions for existence and uniqueness of the maximum are well known [616]. The
pseudosco re
/(
θ)LRL(θ) is an unbiased estimating function, so that the estimates are con sistent
and asymptotically ...
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Publisher Resources

ISBN: 9781482210217