Transitive geostatistics differ essentially from the more familiar
intrinsic geostatistics by being design-based instead of model-based. This
means that the estimator of the mean of the regionalized variable (for
example) is unbiased with respect to all possible samples that could have
been drawn rather than over realizations of a model for a random variable.
Transitive goestatistics then necessitates random sampling while intrinsic
geostatics necessitates nothing of the sort, at least for inferential
I am interested in estimation(1) of the area covered by a regionalized
variable, rather in the mean value or the total. Intrinsic geostatistics
does not allow a 'border effect': the field over which the stochastic
process runs has to be known in advance, so the area cannot be estimated as
a product of intrinsic geostatistical estimation. Transitive geostatistics
does allow for a border effect and then the area can be estimated, in
principle. I have read that the trick is to use the indicator variable
transformation (all values higher than zero must be set equal to 1) and
then estimate the total with transitive geostatistics.
Before i set out to perform such an exploit i would like to know if any of
you knowledgeable people agree on what i wrote above or am i too far off
the truth, and if any of you have applied these techniques or know about
papers in your area of application where this has been performed.
And happy birthday AI-GEOSTATS!
(1) by estimation i mean both an estimator of the expected value and the
variance of the estimator of the expected value.
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