A hierarchical Bayesian model for the analysis of space-time air pollutant concentrations and an application to air pollution analysis in Northern China

Air pollution has been an environmental problem exerting serious impact on human health. An accurate prediction of air pollutant concentrations in space and time is essential to the mitigation and minimization of exposure to air pollution, particularly in cities. To take advantage of data collected at monitoring stations and the effect of secondary information such as meteorological factors, this paper proposes a flexible hierarchical Bayesian model (HBM) which can predict air pollutant concentrations in space and time. Within the framework, spatial temporal Kriging (STK) is employed for interpolation and the obtained results are used as priors. Because of the undesirable performance of the STK, the likelihood in the form of a nonlinear regression (NLR) with skewed normal residuals is employed to take into account the effect of meteorological factors to derive the posterior distribution of air pollutant concentrations. Due to high dimensionality and complexity, the formulation of the posterior distribution is non-analytic. We thus need to draw samples from the estimated parameters of the posterior distribution with Markov chain Monte Carlo (MCMC) method, and approximate the population characteristics with the sample characteristics. We evaluate the HBM with the concentrations of air pollutants and the meteorological variables from Northern China. For all pollutants, in the cross-validation (CV) experiments, the HBM reduces the root mean square error (RMSE) of NLR and STK by at least 0.08 and 0.4, and R² by at least 0.02 and 0.4. The empirical results show that the proposed HBM generally outperforms the NLR and STK in terms of efficiency, accuracy and robustness. The proposed framework is general enough for the analysis of spatial-temporal data of all kinds.