ABSTRACT

Space-time kernel density estimation (STKDE) commonly is used for space-time cluster detection. But, this technique might be limited because it does not take into account an underlying population at risk for observed events. A space-time relative risk function (STRRF) can help overcome this limitation by allowing a comparison of each kernel density of observations with that of controls. This paper proposes a cross-STRRF to identify spatio-temporal locations that experience statistically significant changes in their density of events. With events organized in a space-time voxel structure, the cross-STRRF evaluates space-time patterns by comparing event occurrences at a spatial location in a previous time period with ones in its future as well as with its spatial neighbors in its contemporaneous time period. The test statistics of the cross-STRRF values in each voxel are obtained with a permutation test in which cases and controls are shuffled within each time period to maintain the space-time envelope of events. An application to assault crime incidents in the city of Plano, Texas between 2008 and 2012 illustrates that the cross-STRRF and its significance test results emphasize spatio-temporal changes in event density rather than constantly focusing on high density regions, which STKDE does.

摘要

空时内核密度估计（STKDE）通常用于空时群集检测。但是，此技术可能会受到限制，因为它没有考虑到可能发生观察到的事件的潜在人群。时空相对危险度函数（STRRF）可以通过比较观察值与对照值的每个内核密度来帮助克服此限制。本文提出了一个跨STRRF来识别时空位置，这些时空位置在事件密度方面发生统计上显着的变化。通过以时空体素结构组织事件，cross-STRRF通过比较前一时间段中某个空间位置上的事件发生与未来以及未来那个时间段中与空间邻居发生的事件进行比较，来评估时空模式。 。通过置换测试获得每个体素中的交叉STRRF值的测试统计数据，在这种测试中，在每个时间段内对案例和控件进行混洗以保持事件的时空包络。德克萨斯州普莱诺市在2008年至2012年之间对攻击犯罪事件的一项应用说明，跨STRRF及其重要性测试结果强调事件密度的时空变化，而不是像STKDE那样始终关注高密度区域。