Page 11 - Modern Spatiotemporal Geostatistics
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x Modern Spatiotemporal Geostatistics
a deeper understanding of a theory of knowledge is an important prerequisite
for the development of improved mathematical models of scientific mapping. A
spatiotemporal map, e.g., should depend on what we know about the natural
variable it represents, as well as how we know it (i.e., what sources of knowledge
we selected and what kinds of methods we used to process knowledge). As is
discussed in the book, modern geostatistical approaches can be developed that
are consistent with the above epistemic framework. The main focus of the book
is the Bayesian maximum entropy (BME) approach for studying spatiotempo-
ral distributions of natural variables. As part of the modern spatiotemporal
geostatistics paradigm, the BME approach provides a fundamental insight into
the mapping problem in which the knowledge of a natural variable, not the
variable itself, is the direct object of study. This insight plays a central role in
numerous scientific disciplines. BME's rich theoretical basis provides guidelines
for the adequate interpretation and processing of the knowledge bases avail-
able (different sorts of knowledge enter the modern geostatistics paradigm in
different ways). It also forces one to determine explicitly the available physi-
cal knowledge bases and to develop logically plausible rules and standards for
knowledge integration and processing. BME is formulated in a rigorous way
that preserves earlier geostatistical results, which are its limiting cases, and also
provides novel and more general results that could not be obtained by classical
geostatistics. Indeed, a number of situations are discussed in the book in which
BME's quest for greater rigor serves to expose new, hitherto ignored possibil-
ities. In addition, the presentation of the quantitative results, with their full
technical beauty, is combined with an effort to communicate across the various
fields of natural science. Finally, an attempt has been made to ensure that the
case studies considered in this book involve data that are publicly accessible, so
that all hypotheses made and conclusions drawn can be critically examined and
improved by others (in fact, a scientific model gains authority by withstanding
the criticism of other scientists). Naturally, ideas and practical suggestions on
how to efficiently apply BME theory will evolve as more case studies are done.
Metaphorically speaking, the aim of modern spatiotemporal geostatistics
is to integrate effectively the powerful theoretical perspective of the "Reason of
Plato" (who proposed a conceptual framework that dominated mathematical
reasoning and philosophical thinking for thousands of years) with the practical
thinking of the "Reason of Odysseus" (who was always capable of coming
up with smart solutions to all kinds of practical problems he faced during his
long journey). It has been said that "Plato shared his perspective with the
Gods and Odysseus with the foxes." The modern geostatistician shares it with
both! At this point, I must admit to using these great men as a provocative
and authoritative means of setting things up and getting readers into the right
mood.
In light of the above considerations, the Ariadne's thread running through-
out the book is that the modern geostatistical approach to real-world problems
is that of natural scientists who are more interested in a stochastic analysis con-
cerned with both the ontological level (building models for physical systems)