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Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học Journal of Biology đề tài: Research Article Improving Density Estimation by Incorporating Spatial Information | Hindawi Publishing Corporation EURASIP Journal on Advances in Signal Processing Volume 2010 Article ID 265631 12 pages doi 10.1155 2010 265631 Research Article Improving Density Estimation by Incorporating Spatial Information Laura M. Smith Matthew S. Keegan Todd Wittman George O. Mohler and Andrea L. Bertozzi Department of Mathematics University of California Los Angeles CA 90095 USA Correspondence should be addressed to Laura M. Smith lsmith@math.ucla.edu Received 1 December 2009 Accepted 9 March 2010 Academic Editor Alan van Nevel Copyright 2010 Laura M. Smith et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 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 norm regularizers 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. 1. Introduction High resolution and hyperspectral satellite images city and county boundary maps census data and other types of geographical data provide much information about a given region. It is desirable to .
