Page 230 - Modern Spatiotemporal Geostatistics

Single-Point Analytical Formulations 211

Figure 10.7. CPU time (sec) of BME estimation on an HP-9000/C160 work-
station.

Naturally, as improvements are made in the computer programming of the
BME techniques, the complexity of the numerical algorithms and the associated
computational costs will continue to decrease.

Generalized Covariance—Hard and Soft Data

Readers unfamiliar with the S/TRF-i//^ theory (Christakos, 1991b, 1992) may
skip this section. We will start by proving a fundamental proposition, which
deals with situations in which the spatiotemporal pattern of the natural variable
under consideration is characterized by spatially nonhomogeneous and tempo-
rally nonstationary variations.
PROPOSITION 10.4: The specificatory knowledge is as described in
Proposition 10.1. The general knowledge consists of the generalized
spatiotemporal covariance of orders v/n between any pair of points in
Pmap = {Pi\ * = !,-•• m, k}. Then, the BME posterior pdf is given by
Equation 6.17 (p. 132) with

and