Accurate spatial prediction and rigorous uncertainty quantification are central to modern spatial epidemiology and environmental risk analysis. We introduce a statistically principled hybrid modelling framework that integrates the nonlinear, attention-based representation learning capabilities of a dynamic Graph Attention Network (GATv2) with a latent Gaussian spatial process from model-based geostatistics (MBG). This framework jointly captures relational dependence encoded in graph structures and continuous spatial dependence governed by physical proximity. We evaluate the proposed model via a controlled simulation study and an applied analysis of malaria prevalence data, comparing its predictive accuracy, calibration, and uncertainty quantification against classical geostatistical models and standalone GATv2 architectures. Our analyses show that GATv2 captures complex nonlinear interactions but fails to account for residual spatial autocorrelation, resulting in miscalibrated predictive distributions. Conversely, geostatistical models provide coherent uncertainty quantification through structured covariance functions yet are constrained by linear predictor assumptions and by their reliance on Euclidean distance to encode spatial structure. By integrating attention mechanisms and nonlinear features with an explicit probabilistic spatial random field, the hybrid model captured the relational dependence, consistently improved predictive accuracy, and provided more realistic uncertainty quantification in both simulation and applied settings. Overall, the findings demonstrate that the hybrid model constitutes a statistically coherent and empirically robust framework for modelling complex spatial and spatio-temporal processes in settings where both distance-based and structure-based dependencies operate.

翻译：准确的空间预测和严格的量化不确定性是现代空间流行病学与环境风险分析的核心。我们提出了一种基于统计原理的混合建模框架，该框架将动态图注意力网络（GATv2）基于非线性和注意力机制的表征学习能力与基于模型的地质统计学（MBG）中的潜在高斯空间过程相结合。该框架共同捕捉了图结构中编码的关系依赖性和由物理邻近性控制的连续空间依赖性。我们通过一项受控仿真研究和一项疟疾患病率数据的应用分析评估了所提模型，并将其预测准确性、校准性和不确定性量化与经典地质统计学模型及独立GATv2架构进行了比较。分析表明，GATv2能够捕捉复杂的非线性交互作用，但未能解释残差空间自相关性，导致预测分布校准不良。相反，地质统计学模型通过结构化协方差函数提供了连贯的不确定性量化，但受限于线性预测假设及其依赖欧几里得距离来编码空间结构的方式。通过将注意力机制和非线性特征与显式的概率空间随机场相结合，混合模型捕捉了关系依赖性，持续提高了预测准确性，并在仿真和应用场景中提供了更现实的不确定性量化。总体而言，研究结果表明，混合模型为在基于距离和基于结构的依赖关系同时发挥作用的场景中建模复杂的空间和时空过程，提供了一个在统计上连贯且在实证上稳健的框架。