Page 35 - Modern Spatiotemporal Geostatistics

16 Modern Spatiotemporal Geostatistics — Chapter 1

it was able to go beyond taxonomy and make theoretical understanding its
primary goal (Harre, 1989; Omnes, 1999). In modern scientific disciplines, such
as bioinformatics, the emphasis progressively switches from the accumulation of
data to its scientific interpretation (Baldi and Brunak, 1998). Also, in genetics
most of the controversial issues regarding the genetic origin of complex human
behavioral patterns are ultimately generated not by inadequate data, but rather
by more difficult explanatory and interpretive issues such as: Can we attribute
some features of the genes if they interact with the environmental (nongenetic)
factors? or, Does linkage analysis establish anything more than correlation?
(see Sarkar, 1998).
In some cases, the reliability of claims presented as scientific can be an
issue of life and death (e.g., DNA maps in capital murder trials). The important
issue here is the scientific content of these claims. Justice Blackmun of the
U.S. Supreme Court wrote that in order for expert testimony to be of real
assistance to the courts, "a valid scientific connection to the pertinent inquiry
as a precondition to admissibility" is required, and the question is "whether
reasoning and methodology properly can be applied to the facts in issue" (U.S.
Supreme Court, 1993). In such cases the important factor is the extent to
which a set of data can be related by a credible theory to the situation at hand.
Viewed from the wrong perspective lacking the support of a sound scientific
theory, even the most accurate data may imply false conclusions. As Foster
and Huber (1999, p. 24) point out in their treatise, Scientific Knowledge
and the Federal Courts: "the history of science records many instances of
precise and accurate measurements being piled up around false conclusions,"
and "facts acquire meaning from the theory (express or implied) in which they
are presented, and in turn they determine what conclusions might be drawn
from a theory." This being the situation within the legal system, it could be
a tough case for the proponents of a theory-free geostatistics to demonstrate
the "practicality" of their recipes if the scientific content of the claims is not
considered reliable by the Federal courts.
Indetermination thesis

The main idea of theory-free analysis (also known as physical model-free anal-
ysis or naive empiricism) is to "let the data speak for themselves"; in other
words, "let the data tell us what the mathematical model is." Theory-free anal-
ysis constitutes a fallacy that is a consequence of the pure inductive framework
mentioned in the previous section. Indeed, what this kind of analysis ignores is
the fundamental fact of scientific reality—called the indetermination thesis—
that, while the mapping "model —> data" is one-to-one (i.e., given a spe-
cific set of physical conditions, a model produces one data set), the mapping
"data —> model" is one-to-many (a data set may be represented by numerous
models). As a matter of fact, this is the way the incompleteness of any system
of models or hypotheses manifests itself, in accordance with Godel's theorem
on the incompleteness of any system of axioms (Nagel and Newman, 1958).