Modelling interoccurrence times between ozone peaks in Mexico City in the presence of multiple change points

In this article we consider the problem of analysing the interoccurrence times between ozone peaks. These interoccurrence times are assumed to have an exponential distribution with some rate lambda > 0 (which may have different values for different interoccurrence times). We consider four parametric forms for lambda. These parametric forms depend on some parameters that will be estimated by using Bayesian inference through Markov Chain Monte Carlo (MCMC) methods. In particular, we use a Gibbs sampling algorithm internally implemented in the software WinBugs. We also present an analysis to detect the possible presence of change points. This is performed using the 95% credible interval of the difference between two consecutive means. Results are applied to the maximum daily ozone measurements provided by the monitoring network of Mexico City. An analysis in terms of the number of possible change points present in the model in terms of different years and seasons of the year is also presented.