A non-homogeneous poisson model with spatial anisotropy applied to ozone data from Mexico City

Abstract

In this work we consider a non-homogenous Poisson model to study the behaviour of the number of times that a pollutant’s concentration surpasses a given threshold of interest. Spatial dependence is imposed on the parameters of the Poisson intensity function in order to account for the possible correlation between measurements in different sites. An anisotropic model is used due to the nature of the region of interest. Estimation of the parameters of the model is performed using the Bayesian point of view via Markov chain Monte Carlo (MCMC) algorithms. We also consider prediction of the days in which exceedances of the threshold might occur at sites where measurements cannot be taken. This is obtained by spatial interpolation using the information provided by the sites where measurements are available. The prediction procedure allows for estimation of the behaviour of the mean function of the non-homogeneous Poisson process associated with those sites. The models considered here are applied to ozone data obtained from the monitoring network of Mexico City.