Page 137 - Modern Spatiotemporal Geostatistics

118 Modern Spatiotemporal Geostatistics — Chapter 5

In view of the preceding analysis, an essential difference between classical
and modern geostatistics could be described as follows: Unlike classical geo-
statistics which essentially capitalized on the techniques of spatial statistics,
the emphasis of modern spatiotemporal geostatistics is on the powerful the-
ories and laws of natural sciences. The implication of this difference is that
modern geostatisticians, rather than being misled by the numerous statistical
models and hypotheses compatible with the data set available, should be able
to weed out the physically incorrect models and hypotheses quickly, and get
on to the next problem with a great deal more confidence about the maps and
conclusions they have drawn. This important feature of modern geostatistics
is usually called strong inference in scientific reasoning theory.
EXAMPLE 5.7: The strong inference situation described above is a familiar one
in science. Molecular biology, e.g., was able to make spectacular progress in a
rather short period of time. As Platt (1964) explained in an article published in
the journal Science, this extraordinary success was due to the fact that, unlike
traditional biology which was relying primarily on taxonomy (i.e., collecting,
describing, and tabulating observational facts), molecular biology capitalized
on the powerful theories of chemistry and the mathematical modeling tools of
theoretical physics.

The BME approach aims at contributing to the continuing dialogue be-
tween scientific theories and experimental results. In this sense, the BME
space/time maps could offer valuable evidence that a theory may need to be
revised or reassessed.

Possible modifications and generalizations
of the prior stage

The epistemic framework of modern spatiotemporal geostatistics is very gen-
eral, thus allowing various modifications of the BME approach. Let us briefly
discuss a few possibilities.
The (p a functions of Equation 5.4 were assumed to be of the form
Otner Vet forms may also be considered, thus
broadening the range of applicability of the BME analysis (the issue was al-
ready raised in Chapter 3, "A mathematical formulation of the general knowl-
edge base," p. 74). In cases where the general knowledge consists of statistical
moments (Example 5.1 above), several methods can be used in place of en-
tropy maximization, including series truncation and orthogonal polynomial
expansion (Christakos, 1992).
When the univariate prior pdf is available (considered to be the same at all
points in space/time), it may be assumed that a transformation of the original
random field into a Gaussian one exists. Using the derived statistics of the
Gaussian field, the approach of Example 5.1 can then be applied to define the
9^-operator. Finally, the operator associated with the original field is obtained
by the inverse transformation (Bogaert et al., 1999).