Air Quality Analysis Using Non-Informative and Weakly Informative Priors for Autoregressive Coefficients in the BSTS Model

Abstract

Understanding the complex dynamics of air quality is crucial for reducing environmental pollution and protecting public health. This study aims to investigate the impact of different prior specifications in Bayesian structural time series (BSTS) modelling on the accuracy of predicting air pollution levels (PM2.5 and PM10) across various monitoring stations. The study examines time series data from 5 July 2017 to 30 June 2019. Two priors are compared: non-informative prior regression coefficients (NIP) and weakly informative prior regression coefficients (WIP). The analysis focuses on forecast accuracy metrics, including observed and predicted standard deviations, relative goodness of fit, and R-squared. The results indicate that both approaches indicate that PM10 is more predictable than PM2.5 at all stations, but WIP has been seen to produce lower MAPEs and RMSEs, as well as tighter credible intervals that reduce forecast uncertainty in most stations. For instance, at station CA13A, for PM2.5, WIP lowers MAPE by 0.34% (from 10.68% to 10.34%) and reduces RMSE by 0.017 (0.391 to 0.374), while R² remains stable at 0.85, and relative gof improves slightly from 0.226 to 0.221. For PM10, Relative gof improves slightly from 0.249 to 0.246. Posterior distributions of coefficients (β) under both prior specifications identified ambient temperature and humidity as significant predictors across stations, confirming that the choice of prior does not drastically change which covariates are important. The WIP specification acts towards a more balanced model through enhancing the inclusion of less dominant predictors. Despite minor discrepancies in coefficient estimates, WIP models provided nuanced advantages in model fit and explanatory power. These findings underscore the importance of prior specifications in Bayesian modelling, offering valuable insights for air quality management and forecasting.