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Abstract：
Spatial clustering detection has a variety of applications in diverse fields, including identifying infectious disease outbreaks, pinpointing crime hotspots, and identifying clusters of neurons in brain imaging applications. Ripley\'s K-function is a popular method for detecting clustering (or dispersion) in point process data at specific distances. Ripley\'s K-function measures the expected number of points within a given distance of any observed point. Clustering can be assessed by comparing the observed value of Ripley\'s K-function to the expected value under complete spatial randomness. While performing spatial clustering analysis on point process data is common, applications to areal data commonly arise and need to be accurately assessed. Inspired by Ripley\'s K-function, we develop the positive area proportion function (PAPF) and use it to develop a hypothesis testing procedure for the detection of spatial clustering and dispersion at specific distances in areal data. We compare the performance of the proposed PAPF hypothesis test to that of the global Moran\'s I statistic, the Getis-Ord general G statistic, and the spatial scan statistic with extensive simulation studies. We then evaluate the real-world performance of our method by using it to detect spatial clustering in land parcels containing conservation easements and US counties with high pediatric overweight/obesity rates.
摘要：
空间聚类检测在各个领域有着广泛的应用,包括识别传染病爆发，精确定位犯罪热点，并在脑成像应用中识别神经元簇。Ripley的K函数是一种流行的方法，用于检测特定距离的点过程数据中的聚类（或分散）。Ripley的K函数测量在任何观测点的给定距离内的点的预期数量。可以通过将Ripley的K函数的观测值与完全空间随机性下的期望值进行比较来评估聚类。虽然对点过程数据执行空间聚类分析是常见的，对区域数据的应用通常会出现，需要准确评估。受里普利的K函数启发，我们开发了正面积比例函数（PAPF），并使用它来开发假设检验程序，以检测区域数据中特定距离的空间聚类和分散。我们将提出的PAPF假设检验的性能与全球Moran\sI统计量的性能进行了比较，盖蒂斯-奥德一般G统计，和空间扫描统计量与广泛的模拟研究。然后，我们通过使用该方法来检测包含保护地役权的地块和儿童超重/肥胖率高的美国县的空间聚类，来评估我们方法的实际性能。
