Page 120 - Modern Spatiotemporal Geostatistics

The Epistemic Paradigm 101

EXAMPLE 4.7: Consider the muInvariable (vector) mapping case briefly dis-
cussed in Comment 4.1 (p. 90). Assume, for simplicity, that we are dealing with
two natural variables X(p) and Y(p), in which case the material conditional
has the form

Then, if X(p) physically or logically implies Y(p), the connection "if, then" of
the material conditional could be considered as causally or deductively valid.
This has important consequences in pollution monitoring and control, and in
environmental health studies involving cause-effect analysis in which \ may
represent environmental exposure and V denotes the resulting health effect
map (see Chapter 9, "Associations between environmental exposure and health
effect," on p. 183). D
We conclude our discussion of map conditionals by noticing that the
examination of spatiotemporal mapping in the light of the map conditionals
introduced in these sections deserves to be studied in more depth by modern
geostatisticians.

The BME Net

As the domain of geostatistics keeps expanding in search of new concepts and
applications, a return to the foundations will be necessary because each of the
two processes nourishes the other. The epistemic component of BME analysis
is concerned with the acquisition, modification, integration, and processing of
knowledge by scientific reasoning and experience. Hence, like most epistemolo-
gies, BME incorporates a varying degree of commitment to both rationalism
and empiricism. At the prior stage, e.g., BME emphasizes the importance
of scientific reasoning, physical theories, and laws in advancing knowledge.
By comparison, the meta-prior and integration stages require good knowledge
based on evidence derived from observations, experience, etc. Conditional
probabilities make explicit the changes in the probabilities of maps in light of
physical knowledge. This makes conditional probabilities especially relevant to
logic and to epistemology in general.
The epistemic method offers a higher set of standards for appraising the
quality of a mapping process based on scientific theories and empirical facts,
and for adjudicating between them. In short, the better the underlying epis-
temic method, the more rational a mapping process is deemed to be. BME
analysis leads us to study the nature of the reasoning frame, and so be fore-
warned of its impress on the physical knowledge to be processed by the frame.
From a scientific reasoning point of view, one may argue that the aim of the
mapping paradigm in this chapter is to constrain induction. This is the pur-
pose of the general knowledge ^-constraints on information maximization at
the prior stage, as well as the specificatory knowledge ,5-constraints on proba-
bility maximization at the integration stage. Constraining can avoid generating
innumerable fruitless maps in the search for useful generalizations.