Page 251 - Modern Spatiotemporal Geostatistics

232 Modern Spatiotemporal Geostatistics — Chapter 12

A comparative study of the BME and MMSE approaches is possible in
terms of three essential concepts of scientific reasoning and methodology: ob-
servational nesting, faIsifiability, and fertility degree. The nesting of a scientific
approach (Newton-Smith, 1981) refers to its ability to include the successes
of its predecessors. Indeed, an essential feature of the BME theory is that it
is formulated in a way that preserves most of the referents of earlier theories,
which are its limiting cases.
EXAMPLE 12.1: As we saw above, MMSE estimation is a special case of the
considerably more general BME mapping approach. In the following section,
we will see that popular geostatistical estimators such as kriging are merely
special cases of BME analysis; these special cases are obtained under restrictive
conditions on the form of the estimator and on the physical knowledge bases
that can be used.
The falsifiability of a scientific approach (Popper, 1962) measures the
extent to which it involves hypotheses and models that can be falsified by
empirical (experimental or observational) evidence. The enterprise of science,
as the falsificationist sees it, consists of the proposal of highly falsifiable hy-
potheses, followed by deliberate and tenacious attempts to falsify them. A
newly proposed approach will be considered worthy of the consideration of sci-
entists if it is more falsifiable than its rival. The superiority of BME over the
MMSE method is, thus, demonstrated on the basis of the relative merits of the
competing methods.
EXAMPLE 12.2: By not taking into consideration the physical laws operative
on a natural process or mechanism, the MMSE estimate could be falsified on
the basis of empirical evidence consistent with the laws. BME, on the other
hand, takes into account the physical laws and allows a complete probabilistic
characterization of the situation in terms of its posterior pdf. As a consequence
BME has considerably higher chances of withstanding tests that falsify MMSE
analysis.

The fertility degree of a scientific approach (Chalmers, 1994) measures
the extent to which the approach contains within it objective opportunities for
critical thinking and development, or the extent to which it opens up new lines
of investigation. In this sense, as is obvious from our discussion so far, the
fertility degree of the BME approach is considerably larger than that of the
MMSE approach.
EXAMPLE 12.3: BME provides a sound epistemic framework for critical think-
ing and expands the study domain to include the observer as well as the ob-
served. Non-Gaussian laws are automatically incorporated. Unlike MMSE anal
ysis (which capitalizes on empirical data-fitting techniques), BME capitalizes
on the powerful theories and laws of natural sciences and incorporates vari-
ous forms of knowledge in a rigorous and systematic manner. Also, BME has
global prediction features (whereas MMSE predictors are most appropriate for
interpolation purposes; Stein, 1999), it allows multipoint mapping, etc.