Heterogeneous graphical model for non-negative and non-Gaussian PM 2.5 data

Studies on the conditional relationships between ${\text{PM}}_{2.5}$ concentrations among different regions are of great interest for the joint prevention and control of air pollution. Because of seasonal changes in atmospheric conditions, spatial patterns of ${\text{PM}}_{2.5}$ may differ throughout the year. Additionally, concentration data are both non-negative and non-Gaussian. These data features pose significant challenges to existing methods. This study proposes a heterogeneous graphical model for non-negative and non-Gaussian data via the score matching loss. The proposed method simultaneously clusters multiple datasets and estimates a graph for variables with complex properties in each cluster. Furthermore, our model involves a network that indicate similarity among datasets, and this network can have additional applications. In simulation studies, the proposed method outperforms competing alternatives in both clustering and edge identification. We also analyse the ${\text{PM}}_{2.5}$ concentrations' spatial correlations in Taiwan's regions using data obtained in year 2019 from 67 air-quality monitoring stations. The 12 months are clustered into four groups: January–March, April, May–September and October–December, and the corresponding graphs have 153, 57, 86 and 167 edges respectively. The results show obvious seasonality, which is consistent with the meteorological literature. Geographically, the ${\text{PM}}_{2.5}$ concentrations of north and south Taiwan regions correlate more respectively. These results can provide valuable information for developing joint air-quality control strategies.