SUMMARYIn this paper, we consider the problem of estimating the number of times an air quality standard is exceeded in a given period of time. A non-homogeneous Poisson model is proposed to analyse this issue. The rate at which the Poisson events occur is given by a rate function λ(t), t ≥ 0. This rate function also depends on some parameters that need to be estimated. Two forms of λ(t), t ≥ 0 are considered. One of them is of the Weibull form and the other is of the exponentiated-Weibull form. The parameters estimation is made using a Bayesian formulation based on the Gibbs sampling algorithm. The assignation of the prior distributions for the parameters is made in two stages. In the first stage, non-informative prior distributions are considered. Using the information provided by the first stage, more informative prior distributions are used in the second one. The theoretical development is applied to data provided by the monitoring network of Mexico City. The rate function that best fit the data varies according to the region of the city and/or threshold that is considered. In some cases the best fit is the Weibull form and in other cases the best option is the exponentiated-Weibull.

The cure fraction models are usually used to model lifetime time data with long-term survivors. In the present article, we introduce a Bayesian analysis of the four-parameter generalized modified Weibull (GMW) distribution in presence of cure fraction, censored data and covariates. In order to include the proportion of "cured" patients, mixture and non-mixture formulation models are considered. To demonstrate the ability of using this model in the analysis of real data, we consider an application to data from patients with gastric adenocarcinoma. Inferences are obtained by using MCMC (Markov Chain Monte Carlo) methods.

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A gravidez na adolescência é um problema de saúde pública comum em todo o mundo. O objetivo deste estudo ecológico é estudar o padrão espacial da associação entre os percentuais de gravidez na adolescência e características socioeconômicas dos municípios do Estado de São Paulo, Brasil. Para isso, foi utilizado um modelo bayesiano com uma distribuição espacial que segue uma estrutura condicional autorregressiva (CAR), baseado em algoritmos Monte Carlo em cadeias de Markov (MCMC). Foram usados dados do Sistema de Informações sobre Nascidos Vivos (SINASC) e do Instituto Brasileiro de Geografia e Estatística (IBGE). Verificou-se que a ocorrência de gravidezes precoces apresentou-se maior nos municípios de menor produto interno bruto (PIB) per capita, com maior incidência de pobreza, de menor tamanho populacional, menor índice de desenvolvimento humano (IDH) e maior percentual de indivíduos com índice paulista de vulnerabilidade social (IPVS) igual a 5 ou 6, ou seja, mais vulneráveis. O estudo demonstra uma estreita associação entre gravidez na adolescência e indicadores econômicos e sociais.

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 λ(t), t ≥ 0, 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.

ABSTRACT. We introduce the Weibull distributions in presence of cure fraction, censored data and covariates. Two models are explored in this paper: mixture and non-mixture models. Inferences for the proposed models are obtained under the Bayesian approach, using standard MCMC (Markov Chain Monte Carlo) methods. An illustration of the proposed methodology is given considering a lifetime data set.

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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.