Page 106 - Modern Spatiotemporal Geostatistics

Physical Knowledge 87
EXAMPLE 3.18: Given hard measurements Xhard °f a natural variable X at
points p hard, a technique (e.g., polynomial fitting or model simulation) can
be used to derive new values at the estimation points p^. The new X-values,
which are uncertain, can be used to develop soft data at these points, such as
probability functions having these values as means.

COMMENT 3.5: Frequently used encodin g methods rely o n a series of ques-

tions to establish points on the soft probability functions (e.g., Morgan and
Henrion, 1990). Asking that the experts provide sound scientific justifi-

cation and reasons for and against judgments can improve the quality of

encoding. In the case of probabilistic logic, the encoding methods usually

involve linear o r nonlinear programming techniques fe.g. , Chandru an d

Hooker, 1999).
Finally, in the case that there is not enough knowledge to yield a probability
law, intervals for probabilities may be introduced, e.g.,
where 0 < o, 6 < 1. In addition to the probabilistic formulation, soft data
may be available in the form of fuzzy statements (e.g., "the temperature is
high" or "the range of excessive contamination is short"). These kinds of
statements as well as fuzzy sets result from the experience one has of reality
and the way one constructs and organizes that knowledge. Fuzzy statements
and sets can be processed by approximate reasoning (i.e., fuzzy logic), and
then defuzzified (e.g., converted into definite values; Tanaka, 1997). Soft
data may also be derived from fuzzy information by means of a-cuts (Klir and
Yuan, 1995). Generally, the soft data obtained from fuzzy information may
have forms similar to the ones mentioned above (interval data, etc.).

Summa Theologica

If the laborious effort of data gathering and processing is going to be valu-
able, it must be combined with careful preliminary planning and a conceptual
groundwork identifying what one is looking for, what it is likely to look like,
and how to find it. As a consequence, general knowledge (in the form of scien-
tific theories, laws, conceptual relationships, e£c.)can play an important role in
the acquisition and integration of specificatory knowledge (in the form of hard
and soft data). Depending on the underlying theory, the same data may be
classified according to a variety of categories. In other words, what we already
know influences what we are going to observe.
Specificatory knowledge may become available from a variety of sources.
In many situations in applied sciences, the uncertain knowledge expressed in
terms of soft data is of vital importance. By limiting oneself to knowledge
that is considered certain beyond doubt, one minimizes the risk of some errors