We propose a Bayesian hierarchical model to address the challenge of spatial misalignment in spatio-temporal data obtained from in situ and satellite sources. The model is fit using the INLA-SPDE approach, which provides efficient computation. Our methodology combines the different data sources in a "fusion"" model via the construction of projection matrices in both spatial and temporal domains. Through simulation studies, we demonstrate that the fusion model has superior performance in prediction accuracy across space and time compared to standalone "in situ" and "satellite" models based on only in situ or satellite data, respectively. The fusion model also generally outperforms the standalone models in terms of parameter inference. Such a modeling approach is motivated by environmental problems, and our specific focus is on the analysis and prediction of harmful algae bloom (HAB) events, where the convention is to conduct separate analyses based on either in situ samples or satellite images. A real data analysis shows that the proposed model is a necessary step towards a unified characterization of bloom dynamics and identifying the key drivers of HAB events.

翻译：我们提出了一种贝叶斯分层模型，以解决原位和卫星来源的时空数据中存在的空间错位问题。该模型采用INLA-SPDE方法进行拟合，实现了高效的计算。通过构建空间和时间域内的投影矩阵，我们的方法论将不同数据源整合到一个"融合"模型中。模拟研究表明，与仅基于原位或仅基于卫星数据的独立模型相比，融合模型在跨时空的预测精度上表现更优。此外，融合模型在参数推断方面通常也优于独立模型。此类建模方法源于环境问题的驱动，我们的具体关注点在于有害藻华（HAB）事件的分析与预测——传统上，这类事件是基于原位样本或卫星图像分别独立进行分析的。一项实际数据分析表明，所提出的模型是实现藻华动态统一表征及识别HAB事件关键驱动因素的必要步骤。