Analyzing ozone concentration by Bayesian spatio‐temporal quantile regression

Ground‐level ozone is 1 of the 6 common air pollutants on which the Environmental Protection Agency has set national air quality standards. In order to capture the spatio‐temporal trend of 1‐ and 8‐hr average ozone concentration in the United States, we develop a method for spatio‐temporal simultaneous quantile regression. Unlike existing procedures, in the proposed method, smoothing across different sites is incorporated within modeling assumptions. This allows borrowing of information across locations, which is an essential step when the number of samples in each location is low. The quantile function has been assumed to be linear in time and smooth over space, and at any given site is given by a convex combination of 2 monotone increasing functions ξ1 and ξ2 not depending on time. A B‐spline basis expansion with increasing coefficients varying smoothly over the space is used to put a prior and a Bayesian analysis is performed. We analyze the average daily 1‐hr maximum and 8‐hr maximum ozone concentration level data of the United States and the state of California during 2006–2015 using the proposed method. It is noted that in the last 10 years, there is an overall decreasing trend in both 1‐hr maximum and 8‐hr maximum ozone concentration level over most parts of the US. In California, an overall a decreasing trend of 1‐hr maximum ozone level is observed whereas no particular overall trend has been observed in 8‐hr maximum ozone level.