本論文利用點過程建模的方式,探討犯罪事件的發生地點在空間分布的特徵,並研究不同型態的犯罪事件發生模式在空間上是否有關聯性,及量化其關聯強度。本研究利用2003年至2015年5月3日舊金山地區的犯罪資料為實例,採用異質卜瓦松點過程來描述犯罪事件發生的隨機機制。由於各類犯罪發生地點有明顯的空間特徵(如集中於人口密集和都市開發程度較高的地區),因此採用thin-plate splines描述 intensity function在二維地理空間上的整體趨勢,另以迴歸關係式連結其他犯罪類型在各地點之局部發生頻率的訊息,以量化不同犯罪發生在空間上的關聯性。在參數估計上,我們採用MLE估計參數,並同時引入兩項regularization以調控模式的選取。針對空間上的整體趨勢,採用L2 regularization以限制intensity在空間變化的平滑度,但採用L1 regularization對不同犯罪類型之個別關聯性做具體的變數挑選,最後依據推論的結果建構犯罪發生頻率的預測平面。

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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舊金山地區的犯罪資料
網站來源: https://www.kaggle.com/c/sf-crime.