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Keywords:

  • Gibbs sampling;
  • Bayesian inference;
  • non-homogeneous Poisson model;
  • multiple change-points;
  • ozone air pollution;
  • Mexico city

Abstract

In this paper, we consider some non-homogeneous Poisson models to estimate the probability that an air quality standard is exceeded a given number of times in a time interval of interest. We assume that the number of exceedances occurs according to a non-homogeneous Poisson process (NHPP). This Poisson process has rate function equation image, equation image, which depends on some parameters that must be estimated. We take into account two cases of rate functions: the Weibull and the Goel—Okumoto. We consider models with and without change-points. When the presence of change-points is assumed, we may have the presence of either one, two or three change-points, depending of the data set. The parameters of the rate functions are estimated using a Gibbs sampling algorithm. Results are applied to ozone data provided by the Mexico City monitoring network. In a first instance, we assume that there are no change-points present. Depending on the adjustment of the model, we assume the presence of either one, two or three change-points. Copyright © 2009 John Wiley & Sons, Ltd.