Page 156 - Modern Spatiotemporal Geostatistics

The Choice of a Spatiotemporal Estimate 137

COMMENT 7.1: Another way of saying th e general BMEmode equation i n
words is that Equation 7.2 leads to a choice of an estimate Xk,mode that

adds the minimum possible amount of information to that already extracted
from the data Xdata! '-e-> ^e choice Xk,mode should minimize the following

information gai n

Equation 7.2 leads to a BME mapping equation, the form of which depends
on the form of the ^-operator assumed (and, thus, the hard and soft data
used). The following examples analyze a few common cases of BMEmode
mapping.

EXAMPLE 7.1: By substituting Equations 5.35 (p. 120) and 6.1 (p. 126) into
Equation 7.1 we find

By substituting Equations 5.35 and 6.3 (p. 127) into Equation 7.1 we get

By substituting Equations 5.35 and 6.8 (p. 130) into Equation 7.1 we find

and by substituting Equations 5.35 and 6.9 (p. 130) into Equation 7.1 we
obtain

All the above equations must be solved for

The results of Equations 7.6-7.9 above are summarized by means of the
following proposition.

PROPOSITION 7.1: For the operators and parameters considered in
Table 6.1 (p. 133), the BMEmode equation is as follows

where the B, D, and E s determine the form of the y s posterior operator
considered, as in Equation 6.17 (p. 132).