Page 33 - Modern Spatiotemporal Geostatistics

14 Modern Spatiotemporal Geostatistics — Chapter 1

• Spatiotemporal random field modeling: The natural variable of interest is
represented in terms of a Spatiotemporal random field, which offers a gen-
eral framework for analyzing data distributed in space/time. This framework
is especially effective mathematically; it allows us to grasp difficult problems,
improve our insight into the physical mechanisms and, thus, enhance our pre-
dictive capabilities.
• Physical knowledge classification: The two primary physical knowledge bases
considered in Spatiotemporal analysis and mapping are general knowledge
(obtained from theories, physical laws, summary statistics, etc.) and speci-
ficatory knowledge (obtained through experience with the specific situation).
• Epistemic paradigm: Modern Spatiotemporal geostatistics is underpinned
by a cogent epistemic foundation which combines the world of empirical data
with the world of theory and scientific reasoning. This is a powerful combina-
tion that leads to a distinctive methodology for the acquisition, interpretation,
integration, and processing of physical knowledge.
The course of each one of these three topical 'elements is substantially
influenced by each of the others, to the extent that they form a net or web of
theoretical and empirical support for modern geostatistics, rather than simply
converging upon it.

Why Modern Geostatistics?

The discussion of the previous section was partially motivated by the follow-
ing question: Why should the data analysis community bother with modern
Spatiotemporal geostatistics when there exist already other alternatives which
are fully developed, such as regression methods, spline functions, basis func-
tions, and trend surface techniques? The answer to this question seems to be
threefold:
1. A general answer is a matter of scientific progress: many of the above
techniques—which have been used for several decades—have reached their
limits, and it is time that novel methods be tried in Spatiotemporal mapping
applications. In fact, this development in the field of geostatistics is the nat-
ural course of all human constructions: the time comes when their limits are
recognized and new methods need to be devised. The latter is a necessary step
for the continuing vitality of a scientific field, and geostatistics should not be
an exception.
2. Another answer to the above question is that the case for the existing
methods would be logically much stronger if one could show that all the
alternatives are less good or even inadequate. This is an important reason for
examining other possibilities.
3. Finally, a more specific answer is that many of the existing methods
suffer from a number of well-documented limitations which modern geostatis-
tics makes a serious effort to eliminate. We have already mentioned some of
these limitations. Due to its importance, the matter deserves further discussion,