Bayesian spatial–temporal modeling of air pollution data with dynamic variance and leptokurtosis

Abstract

Spatial–temporal modeling is commonly used to explain the dependence of environmental and socio-economic variables over space and time. Early published works usually assumed constant second and fourth moments. In this paper, we propose a new spatial time series model with dynamic variance and kurtosis. A distinctive feature of our proposed model is that for variables of interest, the model allows the variability and tail heaviness (which usually are indicated by the level of leptokurtosis) to change over spatial location and time. We establish Bayesian inference for the proposed model and conduct a simulation study to showcase the model’s effectiveness compared with that of a baseline model. Air pollution data from Hong Kong and China’s delta region are analyzed to further illustrate the dynamic variance behavior over time and the heavy-tailed characteristics of observations.