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Lecture 11
October 7, 2003
Further Methods for Point
Pattern Analysis
Bailey and Gatrell
Chapter 4
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Certain types of events will exhibit clustering due to
heterogeneity in the underlying distribution
Variations in Population
e.g disease cases or crimes will tend to cluster
where the population is higher
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In such cases we need to “correct” for the the underlying
variations in the population
Use of Kernel Estimates
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Kernel estimate estimates events per unit area
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Reconsider as estimate of events per unit population
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Divide estimated intensity at location s by an estimate of
population density at s
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How to estimate population density at s?
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Estimations of Population Density
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Can take population count for a census unit and convert to
density by dividing by the census unit area
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For the population density at s, use the population density
for the census unit in which s falls
s
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Population for unit j
Area for unit j
Estimations of Population Density
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Population values
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Estimate of population per
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Locations where
populations are recorded
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Estimations of Events per Unit Population
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Divide estimate of
events per unit area by
population per unit area
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Generally use same kernel and bandwidth for each estimate,
but not necessary
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Good estimates of either alone may not lead to good
estimates of the ratio
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Small changes in the estimates of population density in regions
where value is low lead to large variations in ratio
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 Summer '08
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