With increasing accessibility to Geographical Information Systems (GIS) software, researchers and administrators in public health routinely encounter spatially referenced datasets. When data are compiled as aggregates over areal regions, such as counts or rates across counties in a state, they are called areal data. Spatial models for areal data attempt to deliver smoothed maps by accounting for high variability in certain regions. Subsequently, inferential interest is focused upon formally identifying the “edges” or “boundaries” on the map. Here, boundaries refer to borders between two adjacent regions with vastly dissimilar outcomes, which can assist in ascertaining hidden risk factors driving these disparities. The problem of formally identifying such boundaries on a map is known as areal wombling, so named after a foundational article by Womble (1951), and has been garnering attention among spatial analysts in recent times. This article proposes a class of nonparametric Bayesian models that account for uncertainty at various levels and can formally identify boundaries between vastly discrepant neighbors. We conduct a simulation study to illustrate the new approaches and compare them with existing methods. Our proposed methods are subsequently applied to Pneumonia and Influenza hospitalization maps from the SEER-Medicare program in Minnesota, where we detect and report on county boundaries that separate vastly discrepant outcomes from neighboring regions.

中文翻译：

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用于检测区域参考空间数据集中边界的贝叶斯分层模型

随着地理信息系统 (GIS) 软件的可访问性越来越高，公共卫​​生领域的研究人员和管理人员经常会遇到空间参考数据集。当数据被编译为区域区域的聚合时，例如一个州内各县的计数或比率，它们被称为区域数据。区域数据的空间模型试图通过考虑某些区域的高可变性来提供平滑的地图。随后，推理兴趣集中在正式识别地图上的“边缘”或“边界”上。在这里，边界是指结果截然不同的两个相邻区域之间的边界，这有助于确定导致这些差异的隐藏风险因素。在地图上正式识别这些边界的问题被称为区域摆动，以 Womble (1951) 的一篇基础文章命名，并且最近引起了空间分析师的关注。本文提出了一类非参数贝叶斯模型，这些模型可以解释各个级别的不确定性，并且可以正式识别差异极大的邻居之间的边界。我们进行了一项模拟研究来说明新方法并将它们与现有方法进行比较。我们提出的方法随后应用于明尼苏达州 SEER-Medicare 计划的肺炎和流感住院地图，在那里我们检测并报告县边界，这些边界将与邻近地区的结果截然不同。本文提出了一类非参数贝叶斯模型，这些模型可以解释各个级别的不确定性，并且可以正式识别差异极大的邻居之间的边界。我们进行了一项模拟研究来说明新方法并将它们与现有方法进行比较。我们提出的方法随后应用于明尼苏达州 SEER-Medicare 计划的肺炎和流感住院地图，在那里我们检测并报告县边界，这些边界将与邻近地区的结果截然不同。本文提出了一类非参数贝叶斯模型，这些模型可以解释各个级别的不确定性，并且可以正式识别差异极大的邻居之间的边界。我们进行了一项模拟研究来说明新方法并将它们与现有方法进行比较。我们提出的方法随后应用于明尼苏达州 SEER-Medicare 计划的肺炎和流感住院地图，在那里我们检测并报告县边界，这些边界将与邻近地区的结果截然不同。