Efficient Bayesian Spatio-Temporal Clustering with Autoregressive Product Partition Models

We introduce a computationally efficient Bayesian nonparametric model for spatio-temporal data clustering. The model is applied to the logarithm of weekly PM2.5 concentrations to cluster monitoring sites with similar pollution levels taking into account spatial dependence and temporal variations. We propose an Autoregressive Product Partition Model (ARPPM) prior to model spatial random partitions over time, which can integrate past observations and covariates. The associated MCMC algorithm can be executed in parallel, making it suitable for large longitudinal datasets. We validate the approach using air quality data from Lombardy, demonstrating its ability to identify meaningful clusters reflecting both spatial and temporal pollution trends.