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"Spatial filtering" is a term used to describe the methods that are used to compute spatial density estimates for events that have been observed at individual locations.
The term describes a set of tools for displaying functions estimated from these data points that are distributed in two-dimensional space.
Spatial filtering is a form of data smoothing designed to give us a clearer view of the general, unencumbered by details which do not answer our questions of interest.
Spatial filtering is a non-parametric analysis method which belongs within the field of exploratory spatial analysis which relies, to a large degree, on graphical methods of analysis.
Spatial filters are used when we have no a priori curve to fit to a data series. Instead, we rely on nearby, adjacent, values to estimate the value at a given point. Filters take out variability in a data set while retaining the local features of data. By varying the size of the filter, features in the data that vary at different spatial scales can be differentially removed. Spatial filtering is useful as an exploratory technique for identifying areas that are homogeneous or areas that have larger or smaller values than generally occurs.
Two key concepts:
The kernel is the object that is measured. It may be circular, have uniform weight within its area, and be spaced at a constant distance (g) apart in a regular grid.
The bandwidth (or window) is the size of the area over which measurement is made. Results of spatial filtering of information depend upon the choice of kernel and bandwidth. These choices reflect the (unknown) properties of the density field that is being measured and the number of observations available in each filter area.
The graph of the spatial filtering process is generally a "map" which is a concise representation of the phenomena studied.
Any presentation of the spatial distribution of the density of health events in a population is a model of the data. Features of the distribution are to be explained. The density distribution is the fundamental entity to which the events observed relate. Our concept of disease risk is expressed in terms of expected density. Therefore, the spatial density distribution is not just a convenient presentational device. It is the fundamental entity of interest to us.
Results of spatial filtering are useful for identifying possible models of the data or for analyzing how well a given model fits the observed data.