Page 121 - Modern Spatiotemporal Geostatistics

102 Modern Spatiotemporal Geostatistics — Chapter 4
In practice, in some cases, the same knowledge base may be considered
either at the prior stage or at the meta-prior stage, which is an issue of con-
tinuing debate among science methodologists. Various possibilities may exist,
depending on the situation, but one thing is certain: We always have prior
knowledge, but at different times we treat different knowledge as prior. This
situation allows a certain amount of flexibility in the application of the BME
approach and will be revisited later in this book.
COMMENT 4.6: A fascinating case of prior vs. posterior knowledge wa s in-

troduced by the discovery of non-Euclidean geometries (Chapter 2). From

a logical an d mathematical standpoint there is n o a prior i means o f decid-

ing which kind of geometry does in fact represent the space/time relations

between natural variables in a specific situation. Thus, it is necessary to
appeal to specificatory evidence (experimentation, empirical investigation,

etc.) t o fin d ou t whether the question of geometry can be settled a posteriori.

In a sense, the BME model introduces a sort of net that is built (i.) to
"catch" certain knowledge bases of application-specific interest, and (ii.) to
satisfy a set of rules of logic. Part (i.) of the BME net is concerned with the
external representation of a scientific problem in terms of the physical knowl-
edge bases. On the other hand, the main focus of part (ii.) is on how to order
these knowledge bases internally and the relations among them. Therefore,
the twofold goal of the BME net is to acquire various knowledge bases and
to order these bases in an appropriate manner so that when taken all together
they form a realistic picture of the phenomenon of interest. As a consequence
of the twofold goal, map interpretations based on certain knowledge bases and
the examination of the properties of the BME net possess a high level of se-
curity. (However, map interpretations based on the same knowledge bases but
independent of the properties of the BME net should not be considered secure.)
Metaphorically speaking, BME's net somehow resembles the fisherman's net;
by examining the net (properties of the specific BME model used), the fisher-
man (the geostatistician) feels quite secure about the kind offish he can catch
(the map interpretation he can obtain). The sea in which the modern geo-
statistician often throws his net, however, is not any becalmed Sargasso sea,
but one whipped by the winds of uncertainty, governed by complicated physical
phenomena, and teetering on the edge of anomalies and counter-examples.
This chapter has provided a general conceptual account of physical knowl-
edge acquisition and processing rules. The derivation of analytically tractable
mathematical formulations of these rules which hold true in a variety of real-
world applications is the topic of the following chapters.