Statistical models for areal data are primarily used for smoothing maps revealing spatial trends. Subsequent interest often resides in the formal identification of ‘boundaries’ on the map. Here boundaries refer to ‘difference boundaries’, representing significant differences between adjacent regions. Recently, Lu and Carlin (Geogr Anal 37:265–285, 2005) discussed a Bayesian framework to carry out edge detection employing a spatial hierarchical model that is estimated using Markov chain Monte Carlo (MCMC) methods. Here we offer an alternative that avoids MCMC and is easier to implement. Our approach resembles a model comparison problem where the models correspond to different underlying edge configurations across which we wish to smooth (or not). We incorporate these edge configurations in spatially autoregressive models and demonstrate how the Bayesian Information Criteria (BIC) can be used to detect difference boundaries in the map. We illustrate our methods with a Minnesota Pneumonia and Influenza Hospitalization dataset to elicit boundaries detected from the different models.

中文翻译：

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使用贝叶斯信息准则挖掘区域参考空间数据中的边界效应。

区域数据的统计模型主要用于平滑显示空间趋势的地图。随后的兴趣通常在于地图上“边界”的正式识别。这里的边界是指“差异边界”，代表相邻区域之间的显着差异。最近，Lu 和 Carlin (Geogr Anal 37:265–285, 2005) 讨论了一个贝叶斯框架来执行边缘检测，该框架采用空间分层模型，该模型使用马尔可夫链蒙特卡罗 (MCMC) 方法估计。在这里，我们提供了一种避免 MCMC 并且更容易实现的替代方案。我们的方法类似于模型比较问题，其中模型对应于我们希望平滑（或不平滑）的不同底层边缘配置。我们将这些边缘配置合并到空间自回归模型中，并演示了如何使用贝叶斯信息标准 (BIC) 来检测地图中的差异边界。我们用明尼苏达州肺炎和流感住院数据集说明我们的方法，以引出从不同模型中检测到的边界。