A Bayesian non‐linear state space copula model for air pollution in Beijing

Air pollution is a serious issue that currently affects many industrial cities in the world and can cause severe illness to the population. In particular, it has been proven that extreme high levels of airborne contaminants have dangerous short‐term effects on human health, in terms of increased hospital admissions for cardiovascular and respiratory diseases and increased mortality risk. For these reasons, an accurate estimation of airborne pollutant concentrations is crucial. In this paper, we propose a flexible novel approach to model hourly measurements of fine particulate matter and meteorological data collected in Beijing in 2014. We show that the standard state space model, based on Gaussian assumptions, does not correctly capture the time dynamics of the observations. Therefore, we propose a non‐linear non‐Gaussian state space model where both the observation and the state equations are defined by copula specifications, and we perform Bayesian inference using the Hamiltonian Monte Carlo method. The proposed copula state space approach is very flexible, since it allows us to separately model the marginal distributions and to accommodate a wide variety of dependence structures in the data dynamics. We show that the proposed approach allows us not only to accurately estimate particulate matter measurements, but also to capture unusual high levels of air pollution, which were not detected by measured effects.