Improving density estimation by incorporating spatial information

Authors:
Laura M. Smith;Matthew S. Keegan;Todd Wittman;George O. Mohler;Andrea L. Bertozzi
Affiliations:
Department of Mathematics, University of California, Los Angeles, CA;Department of Mathematics, University of California, Los Angeles, CA;Department of Mathematics, University of California, Los Angeles, CA;Department of Mathematics, University of California, Los Angeles, CA;Department of Mathematics, University of California, Los Angeles, CA
Venue:
EURASIP Journal on Advances in Signal Processing - Special issue on advanced image processing for defense and security applications
Year:
2010

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Abstract

Given discrete event data, we wish to produce a probability density that can model the relative probability of events occurring in a spatial region. Common methods of density estimation, such as Kernel Density Estimation, do not incorporate geographical information. Using these methods could result in nonnegligible portions of the support of the density in unrealistic geographic locations. For example, crime density estimation models that do not take geographic information into account may predict events in unlikely places such as oceans, mountains, and so forth. We propose a set of Maximum Penalized Likelihood Estimation methods based on Total Variation and H1 Sobolev normregularizers in conjunction with a priori high resolution spatial data to obtain more geographically accurate density estimates. We apply this method to a residential burglary data set of the San Fernando Valley using geographic features obtained from satellite images of the region and housing density information.