Many models for spatial and spatio-temporal data assume that "near things are more related than distant things," which is known as the first law of geography. While geography may be important, it may not be all-important, for at least two reasons. First, technology helps bridge distance, so that regions separated by large distances may be more similar than would be expected based on geographical distance. Second, geographical, political, and social divisions can make neighboring regions dissimilar. We develop a flexible Bayesian approach for learning from spatial data which units are close in an unobserved socio-demographic space and hence which units are similar. As a by-product, the Bayesian approach helps quantify the relative importance of socio-demographic space relative to geographical space. To demonstrate the proposed approach, we present simulations along with an application to county-level data on median household income in the U.S. state of Florida.

翻译：许多空间和时空数据模型都假定 “物理接近的东西之间相关性更强”，这被称为地理学的第一定律。虽然地理学可能很重要，但并不是全部重要，至少有两个原因。其一，技术有助于缩小距离，以致通过大距离分隔的地区可能会比预期更相似。其二，地理、政治和社会的分裂可能会使相邻的地区不相似。我们开发了一种灵活的贝叶斯方法，用于从空间数据中学习哪些单位在未观察到的社会人口空间中相对接近，因此哪些单位是相似的。作为副产品，贝叶斯方法有助于量化社会人口空间相对于地理空间的相对重要性。为了说明所提出的方法，我们提供了模拟结果以及美国佛罗里达州县级中位数家庭收入数据的应用。