Page 154 - Modern Spatiotemporal Geostatistics

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THE CHOICE OF A SPATIOTEMPORAL
ESTIMATE

"Natural science does not simply describe and explain nature, it is
part of the interplay between nature and scientists." W. Heisenberg

Versatility of the BME Approach

At the integration (or posterior) stage of the BME analysis, estimates must be
determined at the space/time mapping points. BME is a versatile approach
that allows for a variety of possibilities regarding the choice of the appropri-
ate spatiotemporal estimate at the integration stage. As a matter of fact, an
interesting interpretation of the integration stage is obtained in the context
of scientific demonstration, as the latter is understood in natural sciences.
Scientific demonstration—in the wide sense—stands for any experiential ev-
idence that has a large measure of cogency or suasive power relative to a
predictive map. In other words, scientific demonstration may be associated
with specificatory data that lead to a BME estimate with high posterior prob-
ability, or some other desirable feature. Indeed, since the posterior pdf is
rigorously determined through the BME analysis, a large number of options
become available, depending on the physical, economical, and other character-
istics of the application considered. In other words, the BME maps obtained
are case-specific.
Many people will agree that a cogent choice of an estimate is the map that
maximizes the posterior pdf. This choice leads to a BMEmode map which is
described in the following section; a case study involving an extensive porosity
data set is discussed in the section entitled "The West Lyons Porosity Field"
(p. 143). Other choices include maps that optimize the stochastic expectation
(with respect to the posterior pdf) of a function of the natural variable of
interest. Typical examples are the conditional mean estimate (which minimizes

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