Page 41 - Modern Spatiotemporal Geostatistics

22 Modern Spatiotemporal Geostatistics — Chapter 1

Due to its strong epistemic component, BME focuses on levels of spatio-
temporal analysis as they relate to understanding. This is a powerful approach
of scientific reasoning, with particularly appealing features in the mapping of
natural variables (see BME applications in Christakos, 1992, 1998c; Christakos
and Li, 1998; Choi et ai, 1998; Serre et al, 1998; Bogaert et al, 1999; Serre
and Christakos, 1999a; D'Or, 1999). BME features are discussed in detail
in the following sections. To whet the reader's appetite, a brief summary is
provided here.
BME features

From the perspective of modern geostatistics, some of the most appealing
features of BME are as follows (see also discussion on p. 249ff):
• It satisfies sound epistemic ideals and incorporates physical knowledge bases
in a rigorous and systematic manner.
• BME does not require any assumption regarding the shape of the underlying
probability law; hence, non-Gaussian laws are automatically incorporated.
• It can be applied as effectively in the spatial as in the spatiotemporal domains
and can model nonhomogeneous/nonstationary data.
• BME leads to nonlinear estimators, in general, and can obtain well-known
kriging estimators as its limiting cases.
• It is easily extended to functional (block, temporal averages, etc.] and
vector natural variables, and it allows multipoint mapping (i.e., interdependent
estimation at several space/time points simultaneously), which most traditional
mapping techniques do not offer.
• By incorporating physical laws into spatiotemporal mapping, BME has global
prediction features (i.e., extrapolation is possible beyond the range of obser-
vations).
• It is computationally efficient due to the availability of closed form analytical
expressions for certain mapping distributions, etc.

To the above features, one should add BME's beauty which, regretfully,
cannot be captured by words, but can be known only by those who come
sufficiently close to it (which is, of course, the case with any kind of beauty).
In BME analysis, spatiotemporal mapping is viewed as a generalization process
that expresses the important relationship of theory to data. Depending on the
amount of data available, the generalization process may take two forms:
(i.) In many applications only a few data are available. Mapping is then
a process that seeks to create a spatiotemporal pattern by enlarging upon the
limited amount of data available. For the purpose of such an enlargement,
physical knowledge that comes from sources other than direct measurements
becomes extremely important.
(ii.) In several other applications, a huge collection of data must be
confronted, little of which is really relevant to the problem. In this case,