Bayesian areal wombling for geographical boundary analysis
Bayesian areal wombling for geographical boundary analysis
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DOI：
10.1111/j.1538-4632.2005.00624.x
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发表时间：
2005-07-01
影响因子：
3.6
通讯作者：
Carlin, BP
中科院分区：
文献类型：
--
作者：
Lu, HL;Carlin, BP
在空间参考数据的分析中，人们的兴趣通常不是关注空间索引变量本身的预测，而是关注边界分析，即确定地图上分隔较高值和较低值区域的边界。现有的边界分析方法有时被统称为 wombling，以 Womble (195 1) 的一篇基础文章命名。当数据在点级别可用时（例如，疾病病例的精确纬度和经度），通过在拟合空间表面上定位最陡上升或下降的点，最自然地获得这样的边界（Banerjee、Geltand 和 Sirmans 2003）。在本文中，我们提出了区域数据（即仅由地缘政治区域的总和或平均值组成的数据）的相关方法。这些方法对于确定数据集的边界非常有价值，可能出于保密考虑，这些数据集只能以生态（聚合）格式提供，或者只能以这种方式收集（例如，提供医疗保健或成本信息）。在对现有算法技术（包括在商业软件 BoundarySeer 中实现的算法技术）进行简要回顾后，我们提出了一个完全基于模型的区域子宫运动框架，使用贝叶斯分层模型，并使用马尔可夫链蒙特卡罗方法计算后验摘要。我们探索了各种现有的分层和空间软件包（特别是 S-pi us 和 WinBUGS）对任务的适用性，并展示了该方法在实用性和平均均方误差行为方面优于现有非随机替代方案。我们还使用在明尼苏达州县级收集的结直肠癌晚期检测数据来说明我们的方法（以及高级建模问题的解决方案，例如同时推理）。
In the analysis of spatially referenced data, interest often focuses not on prediction of the spatially indexed variable itself, but on boundary analysis, that is, the determination of boundaries on the map that separate areas of higher and lower values. Existing boundary analysis methods are sometimes generically referred to as wombling, after a foundational article by Womble (195 1). When data are available at point level (e.g., exact latitude and longitude of disease cases), such boundaries are most naturally obtained by locating the points of steepest ascent or descent on the fitted spatial surface (Banerjee, Geltand, and Sirmans 2003). In this article, we propose related methods for areal data (i.e., data which consist only of sums or averages over geopolitical regions). Such methods are valuable in determining boundaries for data sets that, perhaps due to confidentiality concerns, are available only in ecological (aggregated) format, or are only collected this way (e.g., delivery of health-care or cost information). After a brief review of existing algorithmic techniques (including that implemented in the commercial software BoundarySeer), we propose a fully model-based framework for areal wombling, using Bayesian hierarchical models with posterior summaries computed using Markov chain Monte Carlo methods. We explore the suitability of various existing hierarchical and spatial software packages (notably S-pi us and WinBUGS) to the task, and show the approach's superiority over existing nonstochastic alternatives, both in terms of utility and average mean square error behavior. We also illustrate our methods (as well as the solution of advanced modeling issues such as simultaneous inference) using colorectal cancer late detection data collected at the county level in the state of Minnesota.