Page 144 - Modern Spatiotemporal Geostatistics

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ANALYTICAL EXPRESSIONS OF THE
POSTERIOR OPERATOR

"It is theory which decides what we can observe." A . Einstein
Specificatory Knowledge and Single-Point

Mapping

Underlying the fundamental equation of Chapter 5 (Eq. 5.35; p. 120) is a posi-
tive feedback that takes place between (i.) meta-prior specificatory knowledge
(e.g., in the form of empirical evidence specific to the problem considered),
and (ii.) the prior probability law obtained from the processing of general
knowledge (e.g., in the form of physical laws, scientific theories, engineering
relationships, and statistical models whose validity has already been confirmed
and reaches beyond the specific problem). Despite its theoretical elegance, as
it stands Equation 5.35 may not offer too much to the practitioner of mod-
ern spatiotemporal geostatistics. Its physical meaning and powerful features
emerge when particular cases of the prior and the posterior (or integration)
operators 9£ ar| d 9£, respectively, are worked out.
These two operators represent the geostatistician's state of knowledge
of the phenomenon under study. Analytical forms of the 9£-°perator have
already been considered in the previous chapter. These forms are associated
with a number of important general knowledge sources encountered by the
practicioner in a variety of scientific disciplines. The mathematical formulation
of the ^-operator depends upon the form in which the specificatory knowledge
base S may become available. Analytical expressions of the ^-operator which
account for some of the most common sources of specificatory knowledge will
be developed in this chapter. Other, more complex situations can be studied
building on these well-understood analytical % expressions. The presentation
of the analytical results, with their full technical beauty, is combined with an

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