In this paper, we propose a Bayesian matrix-variate spatiotemporal modeling framework for jointly analyzing multiple response variables observed at spatial locations over time. The approach relaxes the standard assumption of spatial isotropy by incorporating a deformation-based mechanism, allowing the covariance structure to capture directional effects and nonstationary spatial dependence. Temporal dynamics are modeled through dynamic linear models, enabling coherent uncertainty propagation within a state-space formulation. Missing observations are handled via a data augmentation strategy that preserves the joint structure of the multivariate responses. The proposed methodology is evaluated through simulation studies and an application to air quality data. Results indicate that accounting for spatial deformation leads to substantial gains in predictive performance in anisotropic settings, while cross-variable dependence plays a secondary role in improving overall fit. The framework is computationally tractable for moderate numbers of spatial locations and responses, and provides a flexible basis for modeling multivariate spatiotemporal processes under incomplete data.

翻译：本文提出了一种贝叶斯矩阵变量时空建模框架，用于联合分析随时间在空间位置上观测到的多个响应变量。该方法通过引入基于变形的机制，放松了空间各向同性的标准假设，使协方差结构能够捕捉方向效应和非平稳空间依赖。时间动态通过动态线性模型进行建模，能够在状态空间公式中实现连贯的不确定性传播。缺失观测通过数据增强策略处理，该策略保留了多元响应的联合结构。所提出的方法通过模拟研究和空气质量数据应用进行评估。结果表明，在各向异性设置下，考虑空间变形能显著提升预测性能，而跨变量依赖在改善整体拟合方面起次要作用。该框架在中等数量的空间位置和响应下具有计算可行性，并为在不完全数据下建模多元时空过程提供了灵活的基础。