Bayesian spatio-temporal quantile regression modeling of NO2 with insights for preferential sampling

Air pollution remains one of the most pressing environmental and public health challenges, particularly in the analysis of extreme exposures that are dangerous for human health. Moreover, its monitoring is often limited by the sparse and non-random distribution of ground stations. These stations are often located in areas already known to have higher pollution levels or, alternatively, they are placed in background conditions to serve as a benchmark useful for comparisons. Ignoring this characteristic can lead to biased exposure estimates and unreliable predictions. Moreover, traffic related pollutants such as NO2 are extremely affected by meteorological variables, autoregressive and seasonal components and spatial proxies for human activity. 
Trying to account for all these different realities while modeling the right tail of the distribution represents an important statistical challenge. In this context, quantile regression provides a flexible framework which, when implemented within a Bayesian MCMC setting, is capable of modeling spatio-temporal dependence. However, the issue of preferential sampling has so far been largely overlooked in this context. Our contribution is to model NO2 measured at 34 monitoring stations along the Lazio region of Italy in the period 2011-2022. Monitoring sites were categorized according to a dual Background-Traffic scheme, reflecting the two distinct preferential sampling regimes accounted for in the study. Up to now, we ran NO2 Bayesian quantile regression models introducing fixed effects to underline the impact of external covariates and random effects to account for spatial adjustments. Moreover, we ran preliminary Poisson point processes to provide introductory intensity estimates for station density as exploratory tools. Current and future developments mainly concern the incorporation of the Background-Traffic distinction within the preferential sampling framework, as well as the corresponding update of the MCMC algorithm to accommodate this extension.