Page 214 - Modern Spatiotemporal Geostatistics

Modifications of BME Analysis 195

The main goal of Examples 9.14 and 9.15 above was to demonstrate the
significant advantages of the rigorous spatiotemporal BME modeling of human-
exposure systems and discuss the practical usefulness of a novel stochastic crite-
rion in assessing exposure-health-effect associations. In conclusion, BME anal-
ysis can provide important new insights into human-exposure phenomena, pos
sibly leading to improved environmental exposure-health-effect assessments.
Human-exposure problems, viewed as stochastic spatiotemporal systems, pro-
vide models which may challenge certain assumptions of traditional exposure
analysis, and could shed light on some environmental pollution-population
damage associations now coming under study.

Bringing Plato and Odysseus Together

As is clear from our discussion so far, the modern geostatistics paradigm is an
open system that integrates (i.) epistemic rules, (ii.) physical knowledge, and
(Hi.) control variables and multiple objectives which depend on the applica-
tion being considered. In other words, BME analysis takes place in a spiral
form within which knowledge bases are developed recursively; it is their inte-
gration that guarantees the openness of the system and enables it to evolve
within the limits (physical, economic, etc.) specified by the application under
consideration.
All this points toward the development of a "reality checklist" regarding
the necessary steps that must be taken and the appropriate decisions that need
to be made by the modern geostatistician confronted with real-world problems.
Such a checklist is summarized below:
Step 1. Obtaining a deeper ontologic and epistemic understanding of the phe-
nomenon of interest, the resources, and the procedures available, including:
(a) the spatiotemporal geometry of the study domain (Euclidean vs. non-
Euclidean, intrinsic vs. extrinsic, coordinate system, metric, etc.);
(b) the main physical characteristics of the natural variables involved (spatial
homogeneity, anisotropy, temporal stationarity, additive or non-additive,
small- vs. large-scale variability, etc.);
(c) the knowledge bases available (physical laws, space/time statistics, hard
data, soft data, etc.); and
(d) the operationally defined measurement and sampling procedures (sample
shapes and sizes, sampling networks, etc.).
Step 2. Deciding what kind of S/TRF best represents the natural variables.
This decision should involve the consideration of a number of issues, as follows:
(a) ordinary or generalized models, multiple-point statistics;
(b) permissible correlation functions (covariance, variogram, etc.); and
(c) discrete or continuous representations.