Dataset for: Bayesian Finite Population Modeling for Spatial Process Settings

We develop a Bayesian model-based approach to finite population estimation accounting for spatial dependence. Our innovation here is a framework that achieves inference for finite population quantities in spatial process settings. A key distinction from the small area estimation setting is that we analyze finite populations referenced by their geographic coordinates (point-referenced data). Specifically, we consider a two-stage sampling design in which the primary units are geographic regions, the secondary units are point-referenced locations, and the measured values are assumed to be a partial realization of a spatial process. Traditional geostatistical models do not account for variation attributable to finite population sampling designs, which can impair inferential performance. On the other hand, design-based estimates will ignore the spatial dependence in the finite population. This motivates the introduction of geostatistical processes that will enable inference at arbitrary locations in our domain of interest.We demonstrate using simulation experiments that process-based finite population sampling models considerably improve model fit and inference over models that fail to account for spatial correlation. Furthermore, the process based models offer richer inference with spatially interpolated maps over the entire region. We reinforce these improvements and demonstrate scalable inference for groundwater Nitrate levels in the population of California Central Valley wells by offering estimates of mean Nitrate levels and their spatially interpolated maps.

本研究提出一种基于贝叶斯模型（Bayesian model）的有限总体估计方法，可考量空间依赖性。本研究的创新之处在于构建了一套可在空间过程场景下实现有限总体统计量推断的分析框架。与小域估计（small area estimation）场景的核心差异在于，本研究的分析对象为通过地理坐标标识的有限总体，即点参考数据（point-referenced data）。具体而言，本研究采用两阶段抽样设计：初级抽样单元为地理区域，次级抽样单元为点参考位置，且假设实测值为某空间过程的部分实现。传统地统计模型（geostatistical models）未纳入有限总体抽样设计所引发的变异因素，这可能会损害推断结果的可靠性；而基于设计的估计量则会忽略有限总体中的空间依赖性。这一局限促使我们引入地统计过程，以实现在研究区域内任意位置的推断。本研究通过模拟实验证明，相较于未考量空间相关性的模型，基于过程的有限总体抽样模型可显著提升模型拟合效果与推断精度。此外，基于过程的模型还可生成覆盖全区域的空间插值地图，从而提供更为丰富的推断结果。进一步地，本研究以加利福尼亚中央谷（California Central Valley）的地下水井群体为研究对象，通过估算平均硝酸盐浓度并生成对应的空间插值地图，验证了上述改进效果，并证明该方法可实现规模化推断。