Exposure to high levels of pollution is a persistent problem in large cities throughout the world. The ability to predict the occurrence of a high level of a pollutant allows environmental authorities to take preventive measures, such as controlling the emission of pollution. Communities and officials can also take actions to reduce the exposure of susceptible groups in the population. Therefore, being able to estimate the behavior of a given pollutant is of great importance. In this article we use a Markov chain model to study this behavior. In order to do so, we consider the sequence of the daily maximum measurements of a pollutant and let successive intervals containing them follow a Markov chain of order K>-0. The novelty here is that we allow K to be a random variable and estimate it and the corresponding transition probabilities using a maximum a posteriori method. The results are used to perform estimations about the behavior of ozone levels in Mexico City.

In this work a non-homogeneous Poisson model is considered to study noise exposure. The Poisson process, counting the number of times that a sound level surpasses a threshold, is used to estimate the probability that a population is exposed to high levels of noise a certain number of times in a given time interval. The rate function of the Poisson process is assumed to be of a Weibull type. The presented model is applied to community noise data from Messina, Sicily (Italy). Four sets of data are used to estimate the parameters involved in the model. After the estimation and tuning are made, a way of estimating the probability that an environmental noise threshold is exceeded a certain number of times in a given time interval is presented. This estimation can be very useful in the study of noise exposure of a population and also to predict, given the current behavior of the data, the probability of occurrence of high levels of noise in the near future. One of the most important features of the model is that it implicitly takes into account different noise sources, which need to be treated separately when using usual models.

We consider the problem of estimating the mean and variance of the time between occurrences of an event of interest (inter-occurrences times) where some forms of dependence between two consecutive time intervals are allowed. Two basic density functions are taken into account. They are the Weibull and the generalised exponential density functions. In order to capture the dependence between two consecutive inter-occurrences times, we assume that either the shape and/or the scale parameters of the two density functions are given by auto-regressive models. The expressions for the mean and variance of the inter-occurrences times are presented. The models are applied to the ozone data from two regions of Mexico City. The estimation of the parameters is performed using a Bayesian point of view via Markov chain Monte Carlo (MCMC) methods.