Page 122 - Modern Spatiotemporal Geostatistics

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MATHEMATICAL FORMULATION OF
THE BME METHOD

"Any empirical science in its normal healthy development begins with
a more purely inductive emphasis... and then comes to maturity
with deductively formulated theory in which formal logic and

mathematics play a most significant part." F.S.C . Northro p
A Pragmatic Framework of the Mapping
Problem

The intention of this book is to contribute to a perspective of geostatistics
which is, to a large extent, epistemic. A salient point of the previous chapter
is that the proposed epistemic paradigm places modern spatiotemporal geo-
statistics in a pragmatic framework, the central theses of which are that a
spatiotemporal approach should:
• b e context-dependent (bein g guided b y the physica l knowledg e bases),

• satisf y logically plausible rules , and

• alway s be relevant t o the goals o f the specifi c study .

From the BME mapping viewpoint, the issue is not merely how to deal
with data, but also how to interpret and integrate them into the understanding
process which, as already mentioned, implies that the study domain is expanded
to include the observer (the geostatistician) as well as the observed (a physical
phenomenon).
Consider the spatiotemporal mapping problem described in Chapter 4
(p. 89). Because in many situations the basic problem is the lack of a suffi-
cient number of hard data, bringing diverse sources of general and specificatory
knowledge to bear on mapping can have an especially large payoff. Below we
will follow the steps of the BME epistemic paradigm discussed in Chapter 4
(p. 91) in order to obtain a mathematical solution to the mapping problem.
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