Spatial deformation in a Bayesian spatiotemporal model for incomplete matrix-variate responses

Abstract

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.