Page 268 - Modern Spatiotemporal Geostatistics

Popular Methods in the Light of Modern Geostatistics 249

such as those illustrated by Figure 12.14, arguing that IK is synonymous with
"practicality" may be as realistic as claiming that Chapel Hill is synonymous
with "night life."

Other sorts of kriging
There exist certain other sorts of kriging commonly used in geostatistical data
analysis. Multi-Gaussian kriging (Cressie, 1991) is characterized by the rather
strong assumption that a transformation can be established so that the original
random field can be transformed into a multivariate Gaussian field (a similar
situation was discussed in Example 9.5, p. 174). In multi-Gaussian kriging,
while the original field X(p) may be characterized by a non-Gaussian multi-
variate pdf, it is assumed that a transformation T[-] exists such that the field
1
Y(p) = T~ [X(p)] is multivariate Gaussian. The conditional mean yk \Vdata.
and the variance Var(yk \ydata) can tnen be estimated, which means that
the Gaussian pdf fy(^k l^data) 's completely characterized in terms of these
s
two statistics. Finally, the pdf f x(Xk \Xdata) ' calculated from the Gaussian
pdf. Clearly, in the case in which only hard data are involved, the above pdf
coincides with the BME posterior pdf, i.e., f K(xk) = fx(Xk \ Xdata)- There-
fore, multi-Gaussian kriging is a special case of the general BME analysis.
Additional types of kriging include cokriging and external drift kriging tech-
niques (e.g., Wackernagel, 1995; Batista et ai, 1997). Cokriging and external
drift kriging are useful in cases in which several secondary natural variables in
the mapping of the primary variable must be taken into account. Both tech-
niques share the usual limitations of the MMSE methods; furthermore, they
can only use numerical secondary variables, and the primary and secondary vari-
ables are assumed to be linearly related (Bardosy et al, 1997). Just as for the
previously considered kriging methods, under certain restrictive assumptions,
cokriging and external drift kriging can be derived as special cases of the BME
model (e.g., cokriging is a special case of vector BME, if up to second-order
moments, hard data, and single-point estimation are considered).

Limitations of kriging techniques—Advantages
of BME analysis

It may be appropriate to recall briefly some of the limitations of the kriging
techniques that considerably restrict their theoretical generality as well as their
applicability in practice (more details can be found, e.g., in Goovaerts, 1997;
Christakos, 1998c; Olea, 1999; and Stein, 1999).
(a) It is fairly common practice in the geostatistics literature that the kriging
techniques are restricted to the first- and second-order spatial moments,
as well as hard data available at a set of neighboring points.
(b) Physical laws, high-order space/time moments, and uncertain knowledge
of various forms are not taken into consideration by kriging techniques.