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238 Modern Spatiotemporal Geostatistics — Chapter 12

realizations, i.e ), is plotted. As was expected, eSK(pk) is everywher
larger than
The following example presents some numerical results related to the es-
timation error pdf derived using BME and SK.
EXAMPLE 12.7: Assume that eight measurements of the natural variable
s
X(p), P — ( )£) € R l x T, are available at points Pi~p 8 on a 1 x 1 grid
centered at (0, 0) (as in Fig. 7.1, p. 141). The X(p) has a zero mean and co
2
2
variance c x(h,r) = exp [-0.1257r(/i +r /0.64)]. There is a soft datum at
point p 9 = (s9,tg): the X(p 9) is uniformly distributed within an interval w of
width 0.4. To see how this kind of soft data can improve estimation accuracy at
p k, 1,000 x(pfe)-realizations were generated and pdfs of the estimation errors
have been plotted (Fig. 12.4) for
various positions of p g. The widths of the e BME(p k)-pdfs are clearly smaller
than the width of the eSK(pk)-pdf, implying that XBMs(pk) 's stochastically
more accurate than XsK(Pk)- Naturally, the significance of knowledge at point
decreases as it moves away from p k. At large distances this knowledge has
p 9
little contribution to the estimation at point p k; BME and SK essentially rely
on the same hard data, and BME becomes practically as accurate as SK. D

Figure 12.4. Plots of pdf of estimation errors e BME{p k) and e SK(p k); s 9 =
= 0.2, 0.3, and 0.4.
t g