Geostatistical Discretization and Deconvolution

 

Our new SpaceStat release expands support for kriging methods by adding discretization and deconvolution, providing the ability to perform kriging from one geography to another.  We've also introduced a new graph type, the 2D histogram, which lets you explore how objects are distributed with respect to two variables.

Download a 14-day free trial to see how your research will benefit from using this latest release.  

Why Use Discretization or Deconvolution?

Figure 1. Experimental semivariogram of the risk estimated from county-level rate, and the results of its deconvolution (top curve). The regularization of the point support model yields a curve (short dashed line) that is very close to the experimental one. The model is then used to estimate white female breast cancer mortality risk (deaths/100,000 habitants) and associated prediction variance at the county level (ATA kriging) or at the nodes of a 2 km spacing grid (ATP kriging).

Discretization

The default setting when kriging with polygons is to use the distance between their centroids to determine the covariance between them.  If you instead choose to use a discretization geography or SpaceStat’s random-points method, the pair-wise distances between multiple points in the polygons will be used to calculate their mutual covariance.  This is calculated simply as the average of the covariances for each pair-wise point distance.  This composite estimate is more appropriate than the single estimate based on the centroid distance.

Deconvolution

Deconvolution is a technique for constructing a variogram model for areal data that more accurately describes the spatial processes generating covariance than the model associated with the object centroids.  This deconvolution model should not be understood as the single true model of the underlying spatial process (since this information isn’t known!) but one reasonable possibility.  The procedure is iterative and takes the centroid model of the source geography as a starting point.  If this model is an accurate description of spatial process operating within the polygons then “regularizing” this model should yield back the centroid model.   If the regularized model lies below the centroid model this implies the deconvolution model needs to be moved up with respect to the centroid model.  This process is repeated until the deconvolution model produces a regularized model that lies very close to the centroid model.

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SpaceStat, software for the visualization, analysis, modeling and interactive exploration of spatiotemporal data. (SpaceStat replaces our legacy product STIS, and offers all of the STIS functionality plus many more new features. Additionally, SpaceStat is backwards compatible and able to open your STIS projects.)
ClusterSeer, software for the detection and analysis of event clusters.
BoundarySeer, software for the detection and analysis of geographic boundaries.

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Good luck with your research!

Your BioMedware Team