Bayesian Nonparametric Clustering for Spatiotemporal Data, With an Application to Air Pollution

Air pollution is a major global health hazard, with fine particulate matter (PM10) linked to severe respiratory and cardiovascular diseases. Hence, analyzing and clustering spatiotemporal air quality data is crucial for understanding pollution dynamics and guiding policy interventions. This work illustrates Bayesian nonparametric clustering methods, with a particular focus on their application to spatiotemporal data, which are ubiquitous in environmental sciences. We first introduce key modeling approaches for point-referenced spatiotemporal data, highlighting their flexibility in capturing complex spatial and temporal dependencies. We then provide an overview of recent advancements in Bayesian nonparametric clustering, specifically focusing on spatial product partition models, which incorporate spatial structure into the partition. We illustrate the proposed methods on PM10 data from Northern Italy, demonstrating their ability to identify meaningful pollution patterns by clustering together monitoring stations with similar PM10 dynamics. This paper highlights the potential of Bayesian nonparametric methods for environmental data and offers insights into future research directions in the clustering of spatially referenced time-series data in environmental sciences.