论文标题
测试时空点模式的一阶可分离性假设
Testing the first-order separability hypothesis for spatio-temporal point patterns
论文作者
论文摘要
时空点过程的一阶可分离性在分析时空点模式数据中起着基本作用。虽然通常是一个方便的假设，可以大大简化分析，但在模型构建中应考虑现有的不可分割的结构。我们提出了三种不同的测试，以研究这一假设，作为初步数据分析的步骤。对于泊松过程，前两个测试是精确或渐近的。基于排列和全局信封的第一个测试使我们能够检测到哪个空间和时间位置或滞后数据偏离零假设。第二个测试是一个简单且计算上便宜的$χ^2 $检验。第三个测试基于统计重建方法，通常可以应用于非贫民窟过程。在Poisson和非波森模型的仿真研究中研究了前两个测试的性能。第三个测试应用于2001年英国流行病的真实数据。
First-order separability of a spatio-temporal point process plays a fundamental role in the analysis of spatio-temporal point pattern data. While it is often a convenient assumption that simplifies the analysis greatly, existing non-separable structures should be accounted for in the model construction. We propose three different tests to investigate this hypothesis as a step of preliminary data analysis. The first two tests are exact or asymptotically exact for Poisson processes. The first test based on permutations and global envelopes allows us to detect at which spatial and temporal locations or lags the data deviate from the null hypothesis. The second test is a simple and computationally cheap $χ^2$-test. The third test is based on statistical reconstruction method and can be generally applied for non-Poisson processes. The performance of the first two tests is studied in a simulation study for Poisson and non-Poisson models. The third test is applied to the real data of the UK 2001 epidemic foot and mouth disease.
