A Bayesian Hierarchical Model for the Spatial Analysis of Carbon Monoxide Pollution Extremes in Mexico City

Air pollution by carbon monoxide is a serious problem that affects many cities around the world, and the theory of extreme values has played a crucial role in the study of this issue. In this paper, we proposed a Bayesian hierarchical spatial model of extreme values to evaluate the risk of extreme events of air pollution due to carbon monoxide in the metropolitan area of Mexico City. Spatial trends are modeled through of a Gaussian process for the generalized extreme value (GEV) distribution parameters, and prediction maps are produced for each of these. The results show a marginal spatial behavior for the location, scale, and shape parameters of GEV distribution, which indicate the existence of local variations that would not be possible to model using only stationary models. A return map of the maximum concentrations with a return period of one year is obtained. We found that the return levels for a one-year return period of CO concentration above 8 ppm in the Metropolitan Area of the Valley of Mexico are concentrated in the central part of this region, and the areas with the lowest estimates are distributed in the periphery. In addition, a quantile-quantile (QQ) plot between the theoretical and empirical quantiles was provided, which showed a very good fit of data to the proposed model.