Page 103 - Modern Spatiotemporal Geostatistics

84 Modern Spatiotemporal Geostatistics — Chapter 3

a significant effect on the design and development of a geostatistical
method.
An important consequence of Postulate 3.1 is the well-known support
effect of geostatistics, which is described in the following example.
EXAMPLE 3.13: In many geostatistical applications, the sizes of the opera-
tionally defined measurement units (samples) of a data set are different than
the size of the mapping domain of interest (e.g., a block). This difference
leads to the so-called support effect, which, if not properly taken into consid-
eration, can lead to serious mapping errors. The epistemic nature of the BME
model allows it to be formulated in a way that accounts for the support effect
rigorously and efficiently (see "The support effect" in Chapter 9, p. 168).
Specificatory knowledge in the form of either hard or soft data may be re-
lated to the boundary and initial conditions of a phenomenon; these conditions
are usually complicated, reflecting the complexity of the real world. The con-
struction of high-quality specificatory knowledge bases may entail considerable
investments in time and effort.
Let us now consider separately the two groups of data sets presented in
Equation 3.29 above, and attempt to throw some more light on some of their
most significant features.

Specificatory knowledge in terms of hard data

A scientist or an engineer embarked on any empirical enquiry implements
certain well-established scientific procedures in order to ascertain in a finite
time the knowledge relevant to his/her enquiry. In many of these procedures,
theory-based instruments form the conditions for and are the mediators of a
significant part of scientific knowledge. In this context, the hard data vector
Xhard represents sets of measurements obtained with the help of the instru-
ments which, for all practical purposes, are considered accurate. In real-world
situations, the latter could mean either of the following two things:
(i.) there is a high degree of confidence that the data obtained are not
contaminated by measurement errors, operator biases, computational
blunders, etc.; or,
(ii.) any existing errors are of the sort that can be eliminated effectively by
carefully repeating the operations, successively refining the experimental
techniques, using experience from earlier experiments and theoretical
predictions, etc. (see Bevington and Robinson, 1992, for example).
Since two essential attributes of geostatistical analysis are objectivity and ac-
curacy, the growth of the field should be in a way related to the development
of objectifying instruments which generate accurate hard data. In much of
the following analysis we will suppose that the hard data existing at a set of
m/j (< m) points are represented as follows