Scalable Bayesian Spatiotemporal Tensor Modeling for Censored and Missing Areal Data
We propose a new Bayesian approach for spatiotemporal areal data with censored and missing observations, where the response is represented as a tensor indexed by spatial units and time points. 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. This formulation brings both spatial models into a unified spatiotemporal framework by expressing them as Gaussian Markov random fields in innovation form, providing an interpretable representation of spatial, temporal, and joint spatiotemporal dependence while preserving the multiway structure of the data. The innovation-based structure enables scalable Bayesian implementation in \texttt{Stan} for datasets of moderate size. Simulation studies show that the proposed model outperforms common ad hoc imputation strategies for censored and missing data. We further illustrate its practical value through an application to carbon monoxide (CO) concentrations, where the proposed framework captures complex spatiotemporal dependence in the presence of censoring and missingness.