中文摘要：

对于给定的离散事件数据,可以生成一个概率密度分布图来刻画此类事件发生区域的相对概率.普通的方法如核密度估计法并不考虑与之对应的地理信息.在应用中这类方法会导致离散事件的概率密度出现在不切实际的地理位置.因此,本文提出了新的基于总变差的修正最大罚似然估计方法,不仅可以保证概率估计密度分布的光滑特性,还能确保事件的概率密度不会出现在无效区域.文中运用模拟的离散数据对现有的以及新的方法进行比较来验证新方法的优越性,之后结合真实的地理信息,将该方法运用到某城市的犯罪密度估计当中,验证其对于解决具体问题的可行性并给警方布控以指导.

英文摘要：

Given discrete events data, a probability density map can be produced to model the relative probability of events occurrence. Common methods such as Kernel Density Estimation do not take geographical information into account. In application, these methods could result in the support of probability density appearing in the unrealistic geographical locations. This article proposes Modified Maximum Penalized Likelihood Estimation methods based on Total Variation. It can both ensure the smoothness of the density estimation and guarantee that the density estimation of discrete events do not appear in the invalid location. This article verifies the superiority of the new algorithm by comparing the new algorithm with the traditional through applying simulation discrete data. Then, this article applies this method on criminal density estimation of a city to verify the feasibility of solving actual issue and giving police a guidance on deployment.