Non‐parametric Bayesian covariate‐dependent multivariate functional clustering: An application to time‐series data for multiple air pollutants

Air pollution is a major threat to public health. Understanding the spatial distribution of air pollution concentration is of great interest to government or local authorities, as it informs about target areas for implementing policies for air quality management. Cluster analysis has been popularly used to identify groups of locations with similar profiles of average levels of multiple air pollutants, efficiently summarising the spatial pattern. This study aimed to cluster locations based on the seasonal patterns of multiple air pollutants incorporating the location‐specific characteristics such as socio‐economic indicators. For this purpose, we proposed a novel non‐parametric Bayesian sparse latent factor model for covariate‐dependent multivariate functional clustering. Furthermore, we extend this model to conduct clustering with temporal dependency. The proposed methods are illustrated through a simulation study and applied to time‐series data for daily mean concentrations of ozone (O3$$ {\mathrm{O}}_3 $$), nitrogen dioxide (NO2$$ \mathrm{N}{\mathrm{O}}_2 $$), and fine particulate matter (PM2.5$$ \mathrm{P}{\mathrm{M}}_{2.5} $$) collected for 25 cities in Canada in 1986–2015.