Page 108 - Modern Spatiotemporal Geostatistics

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THE EPISTEMIC PARADIGM

"Whenever one lights upon more exact proofs, then we must be
grateful to the discoverer, but for the present we must state
what seems plausible." Aristotl e (De Caelo, ca. 330 B.C.)

Acquisition and Processing of Physical
Knowledge

To think intelligently, geostatisticians combine empirical reasoning with positive
thinking. As they ponder over the insights their findings are giving them into
"objective reality," they discover that the issue is not merely how to deal with
data but also how to interpret and integrate them into the process of under-
standing and prediction. In a sense, this expands the study domain to include
the observer (geostatistician) as well as the observed (natural processes). The
meaning of such an expansion is that geostatisticians—through the inescapable
demands of their own subjects—are forced to become epistemologists, just as
pure mathematicians have been forced to become logicians. Before proceeding
any further with epistemic analysis, let us formulate a general spatiotemporal
mapping problem of interest in the natural sciences (see also Fig. 4.1):
The spatiotemporal mapping problem: Consider a natural vari-
able X(p) characterized by a set of general knowledge functions as
in Chapter 3, Equation 3.2 (p. 75), and a set of specificatory data
represented by Equation 3.29 later in that chapter (p. 83). We
seek an S/TRF estimator X(p) that provides estimates of the ac-
tual (but unknown) X(p) values at an arbitrary set of space/time
points p kl (e=l,...,p).
While single-point analysis deals with one estimate Xk at a time, multi-
point analysis is concerned with estimates Xk = (Xki, • • • ,Xk p) of \k =
(Xfcu • • • X k p ] at several points p kt ((. = l,...,p) simultaneously. In most
i
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