Generalized spatio-temporal models

An important problem in statistics is the study of spatio-te mporal data taking into account the effect of explanatory variables such as latitude, longitud e and time. In this paper, a new Bayesian approach for analyzing spatial longitudinal data is propos ed. It takes into account linear time regression structures on the mean and linear regression str uctures on the variance-covariance matrix of normal observations. The spatial structure is inc luded in the time regression parameters and also in the regression structure of the variance covaria nce matrix. Initially, we present a summary of the spatial models and the Bayesian methodology u sed to fit the models, as a extension of the longitudinal data analysis. Next, the gene ral spatial temporal model is proposed. Finally, this proposal is used to study rainfall dataPeer Reviewe

Beta Regression Models: Joint Mean and Variance Modeling

In this paper joint mean and variance beta regression models are proposed. The proposed models are fitted applying Bayesian methodology and assuming normal prior distribution for the regression parameters. An analysis of structural and real data is included, assuming the proposed model, together with a comparison of the result obtained assuming joint modeling of the mean and precision parameters

Estadística matemática

IlustracionesEste libro presenta un conjunto de tópicos fundamentales de la Estadística Matemática, cuyo estudio requiere conocimientos de probabilidad, calculo diferencial e integral y calculo vectorial. Está diseñado de tal forma que sirva de base para desarrollar cursos de inferencia estadística de un semestre en programas de matemática, física, ingeniería y estadística. Su principal objetivo es facilitar la apropiación de conceptos estadísticos y, de promover y facilitar el desarrollo de competencias comunicativas, matemáticas y estadísticas, a través de la lectura y análisis de cada una de sus partes. Por esta razón, se recomienda que el estudiante haga la lectura de cada uno de los temas antes de que sean abordados en clase, desarrollando con claridad cada uno de los procesos necesarios para la comprensión total de los temas considerados. Así, las clases podrán ser utilizadas para la discusión de conceptos y procedimientos, para la exposición y discusión de ejercicios, y para el desarrollo de propuestas, métodos alternativos y teorías no incluidas en este documento. (Texto tomado de la fuente).ISBN de la versión impresa 9789587190700Primera edició

Non-Homogeneous Poisson Process to Model Seasonal Events: Application to the Health Diseases

The daily number of hospital admissions due to mosquito-borne diseases can vary greatly. This variability can be explained by different factors such as season of the year, temperature and pollution levels, among others. In this paper, we propose a new class of non-homogeneous Poisson processes which incorporates seasonality factors to more realistically fit data related to rare events, and in particular we show how the modifications applied to the special NHPP intensity function improve the analysis and fit of daily hospital admissions, due to dengue in Ribeirão Preto, São Paulo state, Brazil

Bayesian beta regression models: joint mean and precision modeling

This paper summarizes the beta regression models, with joint modeling of the mean and precision parameters, and the Bayesian methodology proposed by Cepeda (2001) and Cepeda and Gamenrman (2005) to fit these models. This Bayesian methodology is implemented and applied in the development of simulated and applied studies

New volatility models under a Bayesian perspective: a case study

Neste artigo, apresentamos uma breve descrição dos modelos ARCH, GARCH e EGARCH. Normalmente, as estimativas dos parâmetros desses modelos são obtidos através de métodos de máxima verossimilhança. Considerando-se novos processos metodológicos para modelar as volatilidades das séries temporais, precisamos usar outra abordagem de inferência para obter estimativas para os parâmetros dos modelos, uma vez que podemos ter grandes dificuldades para obter as estimativas de máxima verossimilhança, devido à complexidade da função de verossimilhança. Desta forma, obtemos as inferências para as volatilidades das séries temporais sob uma abordagem bayesiana, especialmente com o uso de algoritmos populares de simulação como o método de Monte Carlo em Cadeias de Markov (MCCM). Como uma aplicação para ilustrar a metodologia proposta, analisamos uma série temporal financeira da empresa Gillette variando de janeiro de 1999 à maio de 2003.In this paper, we present a brief description of ARCH, GARCH and EGARCH models. Usually, their parameter estimates are obtained using maximum likelihood methods. Considering new methodological processes to model the volatilities of time series, we need to use other inference approach to get estimates for the parameters of the models, since we can encouter great difficulties in obtaining the maximum likelihood estimates due to the complexity of the likelihood function. In this way, we obtain the inferences for the volatilities of time series under a Bayesian approach, especially using popular simulation algorithms such as the Markov Chain Monte Carlo (MCMC) methods. As an application to illustrate the proposed methodology, we analyze a financial time series of the Gillette Company ranging from January, 1999 to May, 2003

Bayesian structured antedependence model proposals for longitudinal data

An important problem in Statistics is the study of longitudinal data taking into account the effect of other explanatory variables, such as treatments and time and, simultaneously, the incorporation into the model of the time dependence between observations on the same individual. The latter is specially relevant in the case of nonstationary correlations, and nonconstant variances for the different time point at which measurements are taken. Antedependence models constitute a well known commonly used set of models that can accommodate this behaviour. These covariance models can include too many parameters and estimation can be a complicated optimization problem requiring the use of complex algorithms and programming. In this paper, a new Bayesian approach to analyse longitudinal data within the context of antedependence models is proposed. This innovative approach takes into account the possibility of having nonstationary correlations and variances, and proposes a robust and computationally efficient estimation method for this type of data. We consider the joint modelling of the mean and covariance structures for the general antedependence model, estimating their parameters in a longitudinal data context. Our Bayesian approach is based on a generalization of the Gibbs sampling and Metropolis-Hastings by blocks algorithm, properly adapted to the antedependence models longitudinal data settings. Finally, we illustrate the proposed methodology by analysing several examples where antedependence models have been shown to be useful: the small mice, the speech recognition and the race data sets

Gamma regression models with the Gammareg R package

The class of gamma regression models is based on the assumption that the dependent variable is gamma distributed and that its mean is related to a set of regressors through a linear predictor with unknown coefficients and a link function. This link can be the identity, the inverse or the logarithm function. The model also includes a shape parameter, which may be constant or dependent on a set of regressors through a link function, as the logarithm function. In this paper we describe the Gammareg Rpackage, which provides the class of gamma regressions in the R system for their statistical computing. The underlying theory is briefly presented and the library implementation illustrated from simulation studies