Geography Reference
In-Depth Information
points for evaluation can have subtle effects on the results. More specific
control is offered by kriging.
Summary
Geostatistics offers the most complex and important GI analysis operations
because of the underlying power of its mathematically orientated geographic
representations. In geostatics the patterns recorded as GI represent spatial
processes. The mathematical geographic representation is well suited for
analysis of the spatial relationships among complex and diverse indicators
that are beyond direct human interpretation—for example, the analysis of
election results from the over 3,200 U.S. counties. Geostatistics usually works
directly with measurements instead of with cartographic representations.
Work with geostatics therefore requires paying attention to the complexity of
establishing, creating, and validating measurements.
Because of the effects that aggregation to different units—for example,
counties or states—has on measurements, spatial autocorrelation is an impor-
tant issue to keep in mind. Basically, the principle of spatial correlation is
that things are more similar to near things than to faraway things. Classical
statistics assumes, however, that things, no matter where they are, are ran-
domly related to other things.
The Modifiable Areal Unit Problem (MAUP) is the assumption that a
relationship observed at one level of aggregation holds at another, more
detailed, level—for example, that the majority of voters in a city voted for the
candidate who won the state election simply because the candidate won the
state election.
Geostatistics are applied in many areas for many purposes. Archaeolo-
gists doing initial surveys of an area or after collecting data rely on
geostatistics to study possible relationships between data-use terrain analysis.
Chi-square analysis is used as a basic technique to look at the strength of pos-
sible relationships, but is prone to a number of problems arising from
autocorrelation.
In-Depth
Kriging
The arbitrariness of distance-weighting functions used in spatial interpolation
can be addressed by specifying the general form of the function and using
point sample data to determine the exact form. The polynomial equations
make it possible to see clear trends in the data, rather than to fit a rigid struc-
ture to the data with inverse-distance-weighting interpolation.
Kriging is based on a theory of regionalized variables, which means that
distinct neighborhoods have their own variables. This leads to the calculations
being optimized for neighborhoods rather than for the entire area. Kriging
uses inverse-distance-weighting interpolation for each neighborhood, which
can also be varied in a neighborhood. This involves three steps: (1) assessing
the spatial variation of the sample points, (2) summarizing the spatial varia-
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