Page 145 - Modern Spatiotemporal Geostatistics

126 Modern Spatiotemporal Geostatistics — Chapter 6
attempt to communicate across the various fields of natural science. In many
cases, it is still true that "one month on the computer can easily save a day of
paper and pencil research..."; hence, modern geostatisticians should not avoid
using their analytical skills as often as possible. In this chapter, single-point
mapping situations will be considered. Multipoint analysis will be the subject
of later chapters.

Posterior Operators for Interval and
Probabilistic Soft Data

The following proposition considers the common case in which interval soft
data Xsoft are considered at the meta-prior stage.

PROPOSITION 6.1: Assume that the specificatory knowledge S con-
sists of the hard data (Eq. 3.30, p. 84) and the interval (soft) data (Eq.
3.32, p. 85). Then, the posterior operator is given by

where I denotes the domain of xsoft anc' Z 's *ne partition function.
Proof : By definition

Since according to Equation 5.6 (p. 106) f g = Z l exp[9£], Equation 6.2
implies that the posterior operator is given by Equation 6.1. Furthermore,
from Equation 5.35 (p. 120), the posterior pdf is given by

where A = ff dxaoftf§(Xdata) 's tne normalization parameter. D
Equation 6.1 refers to the updated knowledge after the data (hard and
soft) of the meta-prior stage have been incorporated into the analysis. The