Regularized Spatial Point Pattern Analysis with Application to Crime Data
碩士 === 國立清華大學 === 統計學研究所 === 104 === This thesis considered an inhomogeneous Poisson process to characterize the spatial point patterns for the crime events in San Francisco area. The data consist of 39 crimes in Year 2008. We study the global spatial patterns of intensity among different crimes and...
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| Format: | Others |
| Language: | zh-TW |
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2016
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| Online Access: | http://ndltd.ncl.edu.tw/handle/65687008045495243984 |
| Summary: | 碩士 === 國立清華大學 === 統計學研究所 === 104 === This thesis considered an inhomogeneous Poisson process to characterize the spatial point patterns for the crime events in San Francisco area. The data consist of 39 crimes in Year 2008. We study the global spatial patterns of intensity among different crimes and explore possible associations between them. For modeling the intensity functions for all types of crime simultaneously, we use the thin-plate splines to describe the overall intensity baseline function to account for the global and common spatial patterns among crimes. Beyond the global pattern, an extra regression form in terms of the standardized local crime scores are added to the intensity model to capture the specific effects from other crimes. For inference, two types of maximum likelihood estimation (MLE) are implemented: one is based on the detail point data information and the other is based on a coarser block (quadrant) data. Regularization techniques are further incorporated into the likelihood function to smooth the global intensity patterns and to select important association relationship among crimes. Empirical analysis shows a high intensity global patterns centered around the downtown area in San Francisco. It is also found that regularized MLE based on the point data has a higher estimation precision and tends to select a more parsimonious model.
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