This work develops a block aggregation approach to spatial estimation and prediction when the response is observed at a coarse spatial scale, for example as counts of events in administrative areas, or blocks, while covariates are available at a finer spatial resolution, typically as raster images. Our approach specifies a linear predictor at the finer resolution as a combination of covariate effects and a latent, spatially continuous Gaussian process. This linear predictor then determines the distribution of the response through an inverse link function and spatial integration. We use a simulation study to evaluate the performance of the proposed approach in comparison to two industry standard approaches: a traditional geostatistical model that associates each response with the centroid of its block; and a Markov random field (MRF) approach that aggregates covariate data to block-level. As expected, the differences in performance among the three approaches are small with respect to block-level prediction. The rationale for, and advantage of, the block aggregation approach lies in its delivery of reliable inferences at whatever spatial resolution is required in a particular application. We describe two applications: a linear Gaussian sampling model of wastewater virus concentrations in England, using population density as covariate; and log-linear Poisson model of cardiovascular hospitalisations in England using socio-demographic variables at fine-scale administrative units as covariates.

翻译：本研究提出了一种块聚合方法，用于在响应变量以粗尺度空间观测（例如行政区域的计数事件）且协变量以更精细分辨率（通常为栅格图像）可获得时的空间估计与预测。该方法通过将线性预测因子定义为协变量效应与潜在空间连续高斯过程的组合，并利用逆连接函数与空间积分确定响应变量的分布。通过模拟研究，我们评估了所提方法与两种行业标准方法的性能对比：一种是将每个响应与对应区块质心关联的传统地统计学模型；另一种是将协变量数据聚合至区块水平的马尔可夫随机场方法。结果表明，三种方法在区块级预测上的性能差异较小。块聚合方法的理论优势在于能够根据具体应用需求，在任何所需空间分辨率下提供可靠的推断。本文描述了两种实际应用：使用人口密度作为协变量的英格兰废水病毒浓度线性高斯抽样模型；以及以精细尺度行政单元的社会人口变量为协变量的英格兰心血管疾病住院对数线性泊松模型。