We propose a new Bayesian approach for spatiotemporal areal data with censored and missing observations. The method introduces a flexible random effect that combines the spatial dependence structures of the Simultaneous Autoregressive (SAR) and Directed Acyclic Graph Autoregressive (DAGAR) models with a temporal autoregressive component. We demonstrate that this formulation extends both spatial models into a unified spatiotemporal framework, expressing them as Gaussian Markov random fields in their innovation form. The resulting model captures spatial, temporal, and joint spatiotemporal correlations in an interpretable way. Simulation studies show that the proposed model outperforms common ad hoc imputation strategies, such as replacing censored values with the limit of detection (LOD) or imputing missing data by the sample mean. We further apply the method to carbon monoxide (CO) concentration data from Beijing's air quality network, comparing the proposed DAGAR-AR model with the traditional Conditional Autoregressive (CAR) approach. The results indicate that while the CAR model achieves slightly better predictive performance, the DAGAR-AR specification offers clearer interpretability and a more coherent representation of the spatiotemporal dependence structure.

翻译：本文提出了一种针对含删失与缺失观测的时空区域数据的新型贝叶斯方法。该方法引入了一种灵活的随机效应，将同步自回归（SAR）模型与有向无环图自回归（DAGAR）模型的空间依赖结构，与时间自回归分量相结合。我们证明，该公式将两种空间模型扩展为统一的时空框架，并以创新形式将其表达为高斯马尔可夫随机场。所得模型能以可解释的方式捕捉空间、时间及联合时空相关性。模拟研究表明，所提模型优于常见的临时插补策略，例如用检测限（LOD）替换删失值或用样本均值插补缺失数据。我们进一步将该方法应用于北京空气质量监测网络的一氧化碳（CO）浓度数据，将所提出的DAGAR-AR模型与传统的条件自回归（CAR）方法进行比较。结果表明，虽然CAR模型在预测性能上略优，但DAGAR-AR模型在时空依赖结构上具有更清晰的解释性和更一致的表达。