Page 168 - Modern Spatiotemporal Geostatistics

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UNCERTAINTY ASSESSMENT

"Chance is beloved of Art, and Art o f Chance." Aristotl e

Mapping Accuracy

One of the hallmarks of geostatistica! analysis is the determination and report-
ing of the uncertainty attached to our scientific conclusions. This statement
reflects the fact that due to incomplete knowledge, what we actually deter-
mine is a posterior pdf for different realizations of the natural variable. In the
stochastic description of a natural variable in which uncertainty plays a major
role, it is often important to supplement our pdf-based estimates with a sum-
mary assessment of the mapping accuracy. The uncertainty of the BMEmode
estimate, e.g., is a measure of the dispersion of values around the maximum of
the posterior pdf. Assessing the accuracy of maps representing the spatiotem-
poral distribution of natural variables is also of considerable importance to
subsequent stages of the scientific or engineering process related to, e.g., envi-
ronmental risk assessment, multi-objective optimization, and decision making.
The general formula for the posterior pdf is Equation 6.17 (p. 132), which
gives the pdf at each spatiotemporal point p k. The definition of the mapping
accuracy depends on the shape of the pdf. Usually, it can be defined in a
straightforward manner when the posterior pdf has a single maximum. If this
is not the case, the estimation uncertainty should be considered separately for
each maximum. In the case of a pdf with a single maximum, one can further
distinguish between symmetric and asymmetric cases. If the posterior pdf is
symmetric around the maximum, then the maximum coincides with the mean,
etc. In more complex cases, we may need to consider the complete picture
provided by the BME pdf.

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