Page 95 - Modern Spatiotemporal Geostatistics

76 Modern Spatiotemporal Geostatistics — Chapter 3

Table 3.1. The g a functions of Example 3.3.

where K X denotes the generalized covariance of X(p) and n map is the corre-
sponding generalized covariance matrix of the map.
The covariances, variograms, and generalized covariances can have sep-
arable or nonseparable forms (see also "Spatiotemporal Covariance and Var-
iogram Models" in Chapter 11, p. 224). Another interesting situation arising
in practical applications is that in which thep^ statistics contain measurement
errors. Such a situation is discussed in the following example.

EXAMPLE 3.5: Assume that the <fo statistics at the space/time point p (a ^ 0
is the degree of the statistical moment considered) are contaminated by additive
zero-mean white Gaussian measurement errors v a(p)- As a consequence, the
actual ~g^ statistics are related to the measured g a statistics by the relationship

where a. = 1,..., N c. As we shall see in Chapter 5, this is the relationship to
be used in BME analysis.
General knowledge in terms of physical laws

A physical law is a generalization obtained from the scientific study of the
facts of observations. This generalization constitutes a very important Q base,
because it asserts knowledge of what would be the result of an observational