Page 218 - Modern Spatiotemporal Geostatistics

Single-Point Analytical Formulations 199

where

.
is the mean vector for points p t (i = 1, . . , m and fc), and

is the (centered) covariance matrix between all these points.

Proof: Essentially, we need to determine the form of the operator 9£ in Equa-
tion 6.17 (p. 132). Given the general knowledge above, the % is given by

In the following calculations it will be convenient to define the coefficients

In view of Equation 10.6, Equation 5.6 (p. 106) becomes

where and

x
By letting i(> map = X ma.p ~ ma P, the partition function can be written as

Furthermore,

1
where is the ij'-th element of the inverse matrix A and, since
we find