Page 235 - Modern Spatiotemporal Geostatistics

216 Modern Spatiotemporal Geostatistics — Chapter 10

the variance obtained by a numerical quadrature integration scheme for a$ =
0.25. The variance is plotted vs. the dimensionless non-Gaussian perturbation
parameter A = —\I±G\. The estimate O%ER-I 's accurate for A < 0.04.
The estimate cr| )M_ 1 is more accurate than ff^ ER_ 1 for A > 0.04. In fact,
the diagrammatic approach is more accurate than lower-order perturbation for
multivariate distributions as well.

The above approach can be used as well in terms of the posterior pdf
f^(Xk'i Pk)- Such an approach is particularly useful in the calculation of ex-
pectation functionals with respect to the posterior pdf. As we saw in previous
chapters, such functionals arise in a variety of applications, including BME es-
timation (Chapter 7, p. 147), decision making (Chapter 8, p. 163; Chapter 9,
p. 174), and systems analysis (Chapter 9, p. 181).

Theory, Practice, and Computers

The crux of our discussion so far is that BME analysis, just as any scientific
approach, requires reasoning at two levels: (i.) at the theoretical level (which
includes the mathematical formulations and proofs presented in the preceding
sections); and (ii.) at the practical level (which involves computational formu-
lations, cost, efficiency, workable schemes, etc.). At the practical level (ii.), the
efficient implementations of the analytical BME formulations above are made
possible with the help of computers which are capable of collating knowledge
from a number of sources before plotting out the result as a map. SANLIB99
(1999) is the latest version of a continuously updated research library of mod-
ern geostatistics computer programs which can work on any UNIX workstation
network.
Computerized versions of the BME equations take advantage of two dis-
tinct elements of the computer—its ability to store vast amounts of various
forms of knowledge, and its ability to process this knowledge in obedience to
the strict logical procedures of BME analysis. On the basis of theory and
data, the basic BME equations possess significant generalization power. This
generalization may occur at several levels of data availability, extending from
abundance to near absence. At the former level, cautious generalizations can
take place. At the latter level, the generalizations are considerably riskier and
take on the nature of hypotheses.
Our experience so far has been that BME is, indeed, a very good approach
capable of dealing successfully with a variety of practical mapping situations.
Certainly, there is plenty of room for improvement. Improving, e.g., the ef-
ficiency with which physical knowledge is acquired will lead to more rapidly
produced spatiotemporal maps. This will, in turn, speed up the process of
interpretation, understanding, and when necessary, revision.