Page 43 - Modern Spatiotemporal Geostatistics

24 Modern Spatiotemporal Geostatistics — Chapter 1

of reality. Equation 1.5 also acknowledges the importance of studying the in-
ternal relations between the various components of the problem. Furthermore,
the cross-disciplinary interactions inspired by this approach present exciting op-
portunities for fruitful communication between experimentalists and modelers.
The implication of Equation 1.5 is that BME can become a vital component of
an interdisciplinary attack on complex problems. The integration capability
of the BME model is emphasized throughout the book. Some examples related
to environmental health systems are discussed in Chapter 9 (see "BME in the
Context of Systems Analysis," p. 181).

The "Knowledge-Map" Approach

The following chapters elaborate further on each of the BME concepts and
the features briefly discussed in this introductory chapter. We will also address
important practical issues arising in the application of modern spatiotemporal
geostatistics. Particularly, the presentations in this book may be viewed as a
set of "knowledge-maps" that gradually become more detailed.

1. With the first knowledge-map (which includes Chapters 2-4, in which
the ontological and epistemic foundations of modern geostatistics are dis-
cussed), the reader should obtain a general picture of how the BME group
of methods works, without a full grasp of all finer points.
2. The second knowledge-map is more detailed, consisting of the rigorous
mathematical formulation of the BME model (Chapters 5-8). The mathemat-
ics of BME are rather straightforward, which is a useful thing in computational
applications.
3. The third knowledge-map deals with extensions of the BME model
to functional, vector, and multipoint mapping situations (Chapters 9-11). In
Chapter 12, the BME model is compared to some popular mapping methods
both on theoretical grounds and by means of numerical applications.
4. The final "map" that provides a complete understanding of BME is, of
course, for the reader to make: One should try one's own applications!
As a theory of physical knowledge-based spatiotemporal analysis and map-
ping, BME comprises two distinct parts, a formal part focused on mathematical
structure and logical process (formulation and solution of mapping equations,
organization of logical connections, etc.) and an interpretive part concerned
with application of the formal part in real-world situations (choice of natural
language, physical meaning of mathematical terms, methodology, etc.). As
is usual in scientific inquiry, some geostatisticians choose to concentrate their
efforts on the formal part while others prefer to address interpretative aspects.
The two parts influence each other considerably and are equally important to
the development and growth of modern spatiotemporal geostatistics; but, we
must maintain a distinction between their different goals. Much misunder-
standing has been caused by not making the distinction sufficiently clear.