Improving Density Estimation by Incorporating Spatial Information
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...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2010-01-01
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| Series: | EURASIP Journal on Advances in Signal Processing |
| Online Access: | http://dx.doi.org/10.1155/2010/265631 |
| _version_ | 1818146708635254784 |
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| author | Andrea L. Bertozzi George O. Mohler Todd Wittman Matthew S. Keegan Laura M. Smith |
| author_facet | Andrea L. Bertozzi George O. Mohler Todd Wittman Matthew S. Keegan Laura M. Smith |
| author_sort | Andrea L. Bertozzi |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-11T12:23:39Z |
| format | Article |
| id | doaj.art-b3fb007bb9fb45b9a1a7f5e6d779e135 |
| institution | Directory Open Access Journal |
| issn | 1687-6172 1687-6180 |
| language | English |
| last_indexed | 2024-12-11T12:23:39Z |
| publishDate | 2010-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | EURASIP Journal on Advances in Signal Processing |
| spelling | doaj.art-b3fb007bb9fb45b9a1a7f5e6d779e1352022-12-22T01:07:28ZengSpringerOpenEURASIP Journal on Advances in Signal Processing1687-61721687-61802010-01-01201010.1155/2010/265631Improving Density Estimation by Incorporating Spatial InformationAndrea L. BertozziGeorge O. MohlerTodd WittmanMatthew S. KeeganLaura M. SmithGiven 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.http://dx.doi.org/10.1155/2010/265631 |
| spellingShingle | Andrea L. Bertozzi George O. Mohler Todd Wittman Matthew S. Keegan Laura M. Smith Improving Density Estimation by Incorporating Spatial Information EURASIP Journal on Advances in Signal Processing |
| title | Improving Density Estimation by Incorporating Spatial Information |
| title_full | Improving Density Estimation by Incorporating Spatial Information |
| title_fullStr | Improving Density Estimation by Incorporating Spatial Information |
| title_full_unstemmed | Improving Density Estimation by Incorporating Spatial Information |
| title_short | Improving Density Estimation by Incorporating Spatial Information |
| title_sort | improving density estimation by incorporating spatial information |
| url | http://dx.doi.org/10.1155/2010/265631 |
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