Page 289 - Modern Spatiotemporal Geostatistics

270 Modern Spatiotemporal Geostatistics — Chapter 13

Looking back on some of the important geostatistical concepts, many of
them seem simple to us now. Indeed, introducing kriging into spatial estima-
tion was brilliant, but in retrospect it is a simple concept. The same is true for
conditional simulation, etc. So, some geostatisticians may despair, reckoning
that all the good ideas in geostatistics have been discovered and that our only
task is to fill in small gaps here and there. This assessment, however, is not
true. The fact is, there are always opportunities around the corner; the BME
approach is a case in point. As it has been developed so far, BME is the joint
product of theoretical and practical reasoning by which certain of the well-
documented theoretical limitations of the previous geostatistical methods can
be rigorously and efficiently eliminated. The basic BME equations possess sig-
nificant generalization power that takes into account a wide range of knowledge
sources that could not be considered using older methods. The problem-solving
power of BME comes not only from the mathematical formalisms and infer-
ence schemes it utilizes, but from the logical manner in which it processes the
extended knowledge it is able to incorporate. As a result, the spatiotemporal
maps obtained offer a body of information as well as a point of view.
As the domain of modern geostatistics continues to expand in search of
new conquests, the return to its foundations will continue, each of the two
processes nourishing the other. It has become clear that a definite epistemic
outlook is a necessity for developing modern spatiotemporal geostatistics, one
which takes into consideration both the internal and external aspects of ob-
taining and ordering physical knowledge. It is one thing to acquire knowledge
bases, and quite another to organize the various knowledge bases in an ap-
propriate manner so that when taken all together they form a realistic picture
of the phenomenon under investigation. This new outlook is at the core of
BME analysis, supplanting fallacies that have barred progress and becoming
the direct cause of far-reaching advances. Modern spatiotemporal geostatistics
requires blending sufficient skill and depth in stochastic theory and techniques
with substantive knowledge and scientific content. Mathematics and statistics,
because of their ability to account for structure as well as randomness, provide
rigorous representations of spatiotemporal variations and play an important role
in modern spatiotemporal geostatistics. The natural sciences also offer impor-
tant sources of knowledge that can significantly improve the quality of the map
and its scientific interpretation. Last but not least, much depends upon the
insight with which ideas and data are handled before they reach the stage of
mathematics. By making practical application of the epistemic postulates and
conclusions, we subject them to the same sort of observational testing and
control that physical models and assumptions undergo.
The above remarks may be viewed as a "call to research"—an appeal for
establishment of a multidisciplinary conception of modern geostatistics aimed
at novel ideas and models that consider the advances of numerous scientific
disciplines in which geostatistical methods can be applied. Such a conception
of modern spatiotemporal geostatistics should take advantage of the striking
phenomenon of convergence in science and research nowadays. New, highly