Analyzing Ozone Concentration by Bayesian Spatio-temporal Quantile   Regression
  Ground level Ozone is one of the six common air-pollutants on which the EPA has set national air quality standards. In order to capture the spatio-temporal trend of 1-hour and 8-hour average ozone concentration in the US, we develop a method for spatio-temporal simultaneous quantile regression. Unlike existing procedures, in the proposed method, smoothing across the sites is incorporated within modeling assumptions thus allowing borrowing of information across locations, 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 two monotone increasing functions $\xi_1$ and $\xi_2$ 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-hour maximum and 8-hour maximum ozone concentration level data of US and California during 2006-2015 using the proposed method. It is noted that in the last ten years, there is an overall decreasing trend in both 1-hour maximum and 8-hour maximum ozone concentration level over the most parts of the US. In California, an overall a decreasing trend of 1-hour maximum ozone level is observed while no particular overall trend has been observed in the case of 8-hour maximum ozone level. 
Priyam Das and Subhashis Ghosal
stat.ME