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Erschienen in:
2007 | OriginalPaper | Buchkapitel
Spatial prediction
Erschienen in: Model-based Geostatistics
Verlag: Springer New York
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In this chapter, we consider the problem of using the available data to predict aspects of the realised, but unobserved, signal
S
(·). More formally, our target for prediction is the realised value of a random variable
T
=
T
(
S
), where
S
denotes the complete set of realised values of
S
(
x
) as
x
varies over the spatial region of interest,
A
. The simplest example of this general problem is to predict the value of the signal,
T
=
S
(
x
), at an arbitrary location
x
, using observed data
Y
= (
Y
1
, ...,
Y
n
), where each
Y
i
represents a possibly noisy version of the corresponding
S
(
x
i
). Other common targets
T
include the integral of
S
(
x
) over a prescribed sub-region of
A
or, more challengingly, a non-linear functional such as the maximum of
S
(
x
), or the set of locations for which
S
(
x
) exceeds some prescribed value. In this chapter, we ignore the problem of parameter estimation, in effect treating all model parameters as known quantities.