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

Abstract: In this paper, we propose a flexible matrix-variate spatiotemporal model for analyzing multiple response variables observed at spatially distributed locations over time. Our approach relaxes the restrictive assumption of spatial isotropy, which is often unrealistic in environmental and ecological processes. We adopt a deformation-based method that allows the covariance structure to adapt to directional patterns and nonstationary behavior in space. Temporal dynamics are incorporated through dynamic linear models within a fully Bayesian framework, ensuring coherent uncertainty propagation and efficient state-space inference. Additionally, we introduce a strategy for handling missing observations across different variables, preserving the joint data structure without discarding entire time points or stations. Through a simulation study and an application to real-world air quality monitoring data, we demonstrate that incorporating spatial deformation substantially improves interpolation accuracy in anisotropic scenarios while maintaining competitive performance under near-isotropy. The proposed methodology provides a general and computationally tractable framework for multivariate spatiotemporal modeling with incomplete data.