When analyzing spatially referenced event data, the criteria for declaring rates as "reliable" is still a matter of dispute. What these varying criteria have in common, however, is that they are rarely satisfied for crude estimates in small area analysis settings, prompting the use of spatial models to improve reliability. While reasonable, recent work has quantified the extent to which popular models from the spatial statistics literature can overwhelm the information contained in the data, leading to oversmoothing. Here, we begin by providing a definition for a "reliable" estimate for event rates that can be used for crude and model-based estimates and allows for discrete and continuous statements of reliability. We then construct a spatial Bayesian framework that allows users to infuse prior information into their models to improve reliability while also guarding against oversmoothing. We apply our approach to county-level birth data from Pennsylvania, highlighting the effect of oversmoothing in spatial models and how our approach can allow users to better focus their attention to areas where sufficient data exists to drive inferential decisions. We then conclude with a brief discussion of how this definition of reliability can be used in the design of small area studies.

翻译：在分析空间参照事件数据时，关于将发生率声明为“可靠”的标准仍存在争议。然而，这些不同标准的共同点是，在小区分析场景中，粗估计很少能满足这些标准，这促使人们使用空间模型来提高可靠性。尽管这一做法合理，但近期研究已量化了空间统计学文献中常用模型可能过度淹没数据所包含的信息，从而导致过度平滑的程度。在此，我们首先提供一个可用于粗估计和基于模型估计的“可靠”事件发生率定义，该定义允许离散和连续的可靠性声明。随后，我们构建了一个空间贝叶斯框架，使用户能够将先验信息注入模型，以提高可靠性并同时防止过度平滑。我们将该方法应用于宾夕法尼亚州县级出生数据，凸显了空间模型中过度平滑的影响，以及我们的方法如何帮助用户更好地将注意力集中在存在足够数据以驱动推断决策的区域。最后，我们简要讨论了此可靠性定义如何用于小区研究的设计。