Page 221 - Modern Spatiotemporal Geostatistics

202 Modern Spatiotemporal Geostatistics — Chapter 10

PROPOSITION 10.3: The specificatory knowledge is as described in
Proposition 10.1. The general knowledge consists of the variogram
between all pairs of points in space/time. The BMEmode estimate is
the solution of equation

where 7 ifc J is the ifc-th element of the inverse matrix 7 m ^ p such that

is the variogram matrix between the points p i (i — 1, . . . , m) and p k;
and ~x~i(xk) is of the form of Equation 10.15 above with

Proof: The prior pdf is

where and
Since

it follows from Equation 10.24 that A = 2-y map, where the f map is given by
Equation 10.22 above. Equation 7.10 (p. 137) can now be written as

or

with 9£ as in Equation 10.23, which leads to Equation 10.21.