Efficient posterior inference for spatio-temporal modelling of repeated cross-sectional data

Bayesian hierarchical approaches show promise in leveraging extensive datasets, but often lag in computational efficiency, particularly in health surveillance system data analysis. In this context, the continuous collection of population well-being data poses a significant challenge for current methods. While recent approaches demonstrate the capability to model both local and global behaviors, they often prove impractical for continuous updates due to computational demands. Variational methods aim to alleviate these constraints by reducing computational time, yet their approximations may lack accuracy. Our work introduces an alternative variational algorithm, preserving crucial posterior dependencies to enhance reliability. Through meticulous prior specification, we improve the efficiency of variational approximation and facilitate algorithmic steps with closed-form updates. This promising method opens avenues for further exploration of its potential and limitations, inspiring new research directions.