Some Dependence Models for the Time Between Ozone Exceedances in Mexico City

In this paper, we consider several modelling approaches for the mean time between exceedances of a given environmental threshold. The interest here resides in the time between ozone exceedances (also called ozone inter-exceedances times). The proposed models assume two basic density functions for the time between surpassings: the Weibull and the generalised exponential functions. Considering those distributions, a random effect with autoregressive structure is taken into account to determine unexpected changes in the mean of the inter-exceedances density functions. Those unexpected changes could be captured either by their scale parameter or by both their scale and shape parameters. The models are applied to ozone data from the monitoring network of Mexico City. Selection of the model that best explains the data is performed using the deviance information criterion and also the sum of the absolute values of the differences between the estimated and observed means of the inter-exceedances times. An analysis to detect the possible presence of change-points is also presented.     

Using stochastic volatility models to analyse weekly ozone averages in Mexico City

In this paper we make use of some stochastic volatility models to analyse the behaviour of a weekly ozone average measurements series. The models considered here have been used previously in problems related to financial time series. Two models are considered and their parameters are estimated using a Bayesian approach based on Markov chain Monte Carlo (MCMC) methods. Both models are applied to the data provided by the monitoring network of the Metropolitan Area of Mexico City. The selection of the best model for that specific data set is performed using the Deviance Information Criterion and the Conditional Predictive Ordinate method.     

Predator–prey models: an application for the plankton dynamics of lake Geneva

In this paper we present a hierarchical Bayesian analysis for a predator–prey model applied to ecology considering the use of Markov Chain Monte Carlo methods. We consider the introduction of a random effect in the model and the presence of a covariate vector. An application to ecology is considered using a data set related to the plankton dynamics of lake Geneva for the year 1990. We also discuss some aspects of discrimination of the proposed models.     

Use of non-homogeneous Poisson process (NHPP) in presence of change-points to analyze drought periods: a case study in Brazil

Rain precipitation in the last years has been very atypical in different regions of the world, possibly, due to climate changes. We analyze Standard Precipitation Index (SPI) measures (1, 3, 6 and 12-month timescales) for a large city in Brazil: Campinas located in the southeast region of Brazil, São Paulo State, ranging from January 01, 1947 to May 01, 2011. A Bayesian analysis of non-homogeneous Poisson processes in presence or not of change-points is developed using Markov Chain Monte Carlo methods in the data analysis. We consider a special class of models: the power law process. We also discuss some discrimination methods for the choice of the better model to be used for the rain precipitation data.     

Non-homogeneous Poisson models with a change-point: an application to ozone peaks in Mexico city

In this paper, we use some non-homogeneous Poisson models in order to study the behavior of ozone measurements in Mexico City. We assume that the number of ozone peaks follows a non-homogeneous Poisson process. We consider four types of rate function for the Poisson process: power law, Musa–Okumoto, Goel–Okumoto, and a generalized Goel–Okumoto rate function. We also assume that a change-point may or may not be present. The analysis of the problem is performed by using a Bayesian approach via Markov chain Monte Carlo methods. The best model is chosen using the DIC criterion as well as graphical approach.     

Comparing the Number of Ozone Exceedances in Different Seasons of the Year in Mexico City

Ozone air pollution is a serious problem in several cities of the world. Hence, to analyse the behaviour of this pollutant is a very important issue. One problem of interest is to study the behaviour of the inter-occurrences times between two ozone exceedances, i.e. between two days in which the pollutant’s measurement surpasses a given threshold. Another interest resides in comparing the behaviour of ozone measurements in different seasons of the year. In this paper we use some Poisson models to analyse this problem. The time interval at which the ozone measurements were taken is split into subintervals corresponding roughly to the seasons of the year. We consider three parametric forms for the mean of the Poisson model, and consequently for the mean of the inter-occurrences times. In each model, the parameters describing its mean are estimated using Bayesian inference via Markov chain Monte Carlo methods. The models are applied to the ozone measurements provided by the Mexico City monitoring network. Theoretical results suggest that an increase has occurred in the mean inter-exceedances times and this is corroborated by the observed data. Differences between the behaviour of the pollutant during different seasons of the year are also detected as well as similarities in the same season in different years. Besides estimating the mean of the Poisson models, inference for the possible presence and location of change-points indicating change of parameters of the model is also performed.     

Climate Change: Use of Non-Homogeneous Poisson Processes for Climate Data in Presence of a Change-Point

Environmental Modeling & Assessment - In this study, non-homogeneous Poisson processes (NHPP) are used to analyze climate data. The data were collected over a certain period time and consist of...