Page 166 - Modern Spatiotemporal Geostatistics

The Choice of a Spatiotemporal Estimate 147

information subject to constraints representing general knowledge. The inte-
gration stage leads to the maximization of the posterior pdf which incorporates
the specificatory knowledge S- As a consequence, the BME map offers a body
of information as well as a point of view. Surely, BME's efficiency in practi-
cal situations depends on the amount and quality of the physical knowledge
objectively available which, however, does not need to be limited to the forms
processed by the methods of classical geostatistics.

Other BME Estimates

Since the posterior pdf is available through the BME approach, in addition to
the mode estimate, several other choices of an estimate \k are possible as well
(see Fig. 7.7). In fact, as was emphasized in a previous section, the choice of
the appropriate estimate is case specific rather than universal (i.e., it depends
on the physical variables involved in the specific case study, the economic
and topographic constraints, personal preferences, multiple objectives, etc.).
Given the posterior pdf f%(Xk)i °ne may choose as an estimate the median
(BMEmedian)

at each point p k; or, the conditional mean (BMEmeari)

at each point p k. The BMEmedian estimate may be used when one is interested
in assigning equal weights to the underestimation and overestimation cases.
The BMEmean estimate is suitable, e.g., for mapping situations where one
seeks to penalize large errors more than smaller ones. Percentiles, quantiles,
etc. may also be defined from the posterior pdf.

Figure 7.7. Choosing a BME estimate from the posterior pdf.