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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.

In this paper we summarize the main points of beta regression models under Bayesian perspective, including a presentation of the Bayesianbetareg R-package, used to fit the beta regression models under a Bayesian approach. Finally, beta regression models are fitted to a reading score database using, respectively, the Bayesianbetareg and betareg R-Packages for Bayesian and classic perspectives.

In this paper we propose a new residuals for gamma regression models, assuming that both mean and shape parameters, follow regression structures. The models are summarized and fitted by applying both classic and Bayesian methods as proposed by Cepeda-Cuervo. The residuals are proposed from properties of the biparametric exponential family of distributions and simulated and real data sets are analyzed to determine the performance and behavior of the proposed residuals.

Time series models are often used in hydrology and meteorology to model streamflows series in order to make forecasting and generate synthetic series which are inputs for the analysis of complex water resources systems. In this paper we introduce a new modeling approach for hydrologic and meteorological time series assuming a continuous distribution for the data, where both the conditional mean and conditional variance parameters are modeled. Bayesian methods using standard MCMC (Markov Chain Monte Carlo Methods) are used to simulate samples for the joint posterior distribution of interest. Two applications to real data set illustrate the proposed methodology, assuming that the observations come from a normal, a gamma or a beta distribution. A first example is given by a time series of monthly averages of natural streamflows, measured in the year period ranging from 1931 to 2010 in Furnas hydroelectric dam, Brazil. A second example is given with a time series of 313 air humidity data measured in a weather station of Rio Claro, a Brazilian city located in southeastern of Brazil. These applications motivate us to introduce new classes of models to analyze hydrological and meteorological time series.

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.

Time series models are often used in the analysis of Meteorological phenomena to model levels of rainfall, temperature and levels of air humidity series in order to make forecasting and generate synthetic series which are inputs for the analysis of the influence of these variables on the quality of life. Relative air humidity for example, has great influence on the count increasing of respiratory diseases, especially for some age populations as newly born and elderly people. In this paper we introduce a new modeling approach for meteorological time series assuming a beta distribution for the data, where both the mean and precision parameters are being modeled. Bayesian methods using standard MCMC (Markov Chain Monte Carlo Methods) are used to simulate samples for the joint posterior distribution of interest. An example is given with a time series of 313 air humidity observations, measured by a wether station of Rio Claro, a city localized in S˜ao Paulo state, southeastern of Brazil.

This work proposes joint modeling of parameters in the biparametric exponential family, including heteroscedastic linear regression (non linear regression) models; with joint modeling of the mean and precision (the variance) parameters; beta regression models, longitudinal date analysis (including modeling of the covariance matrix) and hierarchical models. This work presents results of the classic approach to fit regression models for both mean and precision parameters in biparametric exponential family of distributions, which includes Bayesian methods for fitting the proposed models. And also extensions of the Bayesian methods to fit nonlinear regression models. Finally, proposes to use a Bayesian approach for modeling the covariance matrix in normal regression models when the observations are not independent. This document includes the following chapters: Chapter 1 is a introduction. Chapter 2 presents a summary of generalized linear models and the classical and Bayesian approaches to the parameters estimation, presenting the Fisher score method and a Bayesian approach using the Metropolis-Hastings algorithm. In Chapter 3, the heteroscedastic normal linear regression models are considered, including summaries of the classic method and Bayesian method proposed to fit these models. Chapter 4 is an extension of Chapter 3, which studies the regression models in the biparametric exponential family of distribution for mean and precision parameters. The following examples are included. 1. Gamma regression models with regression structures in the mean and precision (variance). 2. Beta regression models with regression structures in both mean and dispersion parameter. Several simulation studies were performed to illustrate these models and the proposed Bayesian methods. Chapter 5 discusses normal nonlinear heteroskedastic regression models. Chapter 6 include a Bayesian proposal to fit longitudinal regression models, where regression structures are assumed for the mean and the variance-covariance matrix of observations with Normal distribution (longitudinal data) Chapter 7 presents an extension of the methodology proposed in the previous chapters for adjusting hierarchical models.

In this paper we propose a bivariate beta regression model, de¯ning the beta distribution derived from Farlie-Gumbel-Morgenstern (FGM) copulas. This model could be a good alternative to analyze pairs of proportions, when they are not independent. To ¯t the proposed models we apply standard existing MCMC (Markov Chain Monte Carlo) methods to simulate samples for the joint posterior of interest, using the Bayesian methodology proposed by Cepeda and Gamerman (2001) and Cepeda and Gamerman (2005). Two examples are introduced to illustrate the proposed methodology: an example with simulated bivariate data and an example with a real data set.

In this paper WinBugs code to fit joint mean and precision (variance) beta regression models is presented. These models are fitted applying Bayesian methodology and assuming normal prior distribution for the regression parameters. Analysis of structural data are included, assuming these models.

Gamma regression models are a suitable choice to model continuous variables that take positive real values. This paper presents a gamma regression model with mixed effects from a Bayesian approach. We use the parametrization of the gamma distribution in terms of the mean and the shape parameter, both of which are modelled through regression structures that may involve fixed and random effects. A computational implementation via Gibbs sampling is provided and illustrative examples (simulated and real data) are presented. Resumen Los modelos de regresión gamma son una opción adecuada para modelar variables continuas que toman valores reales positivos. Este artículo presenta un modelo de regresión gamma con efectos mixtos desde un enfoque bayesiano. Utilizamos la parametrización de la distribución gamma en términos de la media y el parámetro de forma, los cuales se modelan a través de estructuras de regresión que pueden involucrar efectos fijos y aleatorios. Se proporciona una implementación computacional a través del muestreo de Gibbs y se presentan ejemplos ilustrativos (datos simulados y reales).

This paper proposes new linear regression models to deal with overdispersed binomial datasets. These new models, called tilted beta binomial regression models, are defined from the tilted beta binomial distribution, proposed assuming that the parameter of the binomial distribution follows a tilted beta distribution. As a particular case of this regression models, we propose the beta rectangular binomial regression models, defined from the binomial distribution assuming that their parameters follow a beta rectangular distribution. These new linear regression models, defined assuming that the parameters of these new distributions follow regression structures, are fitted applying Bayesian methods and using the OpenBUGS software. The proposed regression models are fitted to an overdispersed binomial dataset of the number of seeds that germinate depending on the type of chosen seed androot., 17 pages, 4 figures

Overdispersion is a common phenomenon in count datasets, that can greatly affect inferences about the model. In this paper develop three joint mean and dispersion regression models in order to fit overdispersed data. These models are based on reparameterizations of the beta-binomial and negative binomial distributions. Finally, we propose a Bayesian approach to estimate the parameters of the overdispersion regression models and use it to fit a school absenteeism dataset. La sobredispersión es un fenómeno común en conjuntos de datos de conteo, que puede afectar en alto grado las inferencias relacionadas con el modelo. En este artículo desarrollamos tres modelos de regresión conjunta de media y dispersión para ajustar datos sobredispersos. Estos modelos se basan en reparameterizaciones de las distribuciones beta-binomial y binomial negativa. Finalmente, proponemos un enfoque Bayesiano para la estimación de los parámetros de los modelos de regresión sobredispersos y lo utilizamos para ajustar un conjunto de datos de ausentismo escolar.

Se presenta un nuevo modelo análisis envolvente de dalos temporal que supera algunas debilidades de los modelos análisis de ventana e Índice Malmquist presentados en la literatura. Se construyen series temporales con datos de manufactura proporcionados por el Departamento Administrativo Nacional de Estadística. Para cada serie, se selecciona el mejor de un conjunto de modelos ARIMA y se establecen pronósticos para dos períodos. Se analizan cambios de eficiencia de los cinco centros industriales más grandes de Colombia. La aplicación del nuevo modelo muestra las ventajas que resultan al considerar más de dos períodos. Muestra también cómo se mejora el Malmquist clásico al cambiar variables univariadas determinísticas por series de tiempo. Basado en los resultados se concluye que el método está cerca de ser un análisis envolvente de datos en tiempo real. This paper presents a new temporal data envelopment analysis model that overcomes some weaknesses of the window analysis and Malmquist Index models reported in the literature. Time series are constructed with manufacturing data from the National Administrative Department of Statistics. For each series the best of a set of ARIMA models is selected, and a forecast for two periods is established. Changes in efficiency of the five largest industrial centers of Colombia are analyzed. For that, variables are located at different time positions including forecasts. The implementation of the new model shows the benefits of considering more than two periods. It also shows how classical Malmquist method is improved by changing deterministic univariate variables by time-series. Based on the results it is concluded that the method is close of being a data envelopment analysis in real time.

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.

En este estudio se reanalizaron los datos de Cepeda C., Pacheco Durán, García Barco y Piraquive Peña (2008) mediante un modelo de Teoría de Respuesta al Ítem (TRI), y mediante Análisis de Correspondencias Múltiples (ACM) y de clasificación. Se encontró que las propiedades psicométricas del cuestionario de acoso escolar son bastante buenas (α = 0.96 y buen ajuste al modelo unidimensional a partir del análisis paralelo). Además, se presentan las coincidencias entre los resultados de los dos tipos de análisis, y se encuentran resultados similares a otros estudios en Colombia. Los resultados de este estudio indican que el cuestionario analizado es una medida válida y confiable del acoso en el contexto escolar. This study presents reanalyzes of Cepeda et al. (2008)'s data using an Item Response Theory (IRT) model and Multiple Correspondence Analysis (MCA). Both internal consistency (α = 0.96) and fit to the unidimensionality assumption (per parallel analysis) were found to be satisfactory. Coincidences between both analyses are shown. The percentage of students affected by bullying in the sample is similar to that found in other studies in Colombia. Finally, the questionnaire appears to be a valid and reliable measure of bullying.

In this paper, we present a brief description of multivariate GARCH 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 another inference approach to get estimates for the parameters of the models, since we can have great difficulties to obtain 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 as the Markov Chain Monte Carlo (MCMC) methods. As an application to illustrate the proposed methodology, we analyze log-returns of IBOVESPA and Dow Jones Industrial in a weekly basis from 04/27/1993 to 11/03/2008. En este artículo se presenta una breve descripción de modelos GARCH multivariados y se realizan inferencias de la volatilidad de series de tiempo usando un enfoque Bayesiano, utilizando algoritmos de simulación de Monte Carlo (MCMC). Como una aplicación para ilustrar la metodología propuesta, se analizan los logretornos de IBOVESPA y Dow Jones Industrial en una base semanal de 04/27/1993 para 11/03/2008. Dans cet article on présente une brève description des modèles GARCH multivariés et on fait d'analyse d'inférence sur la volatilité des séries temporelles en utilisant une approche bayésienne et des algorithmes de simulation de Monte Carlo (MCMC). Comme application pour illustrer la méthodologie proposée, on étudie des log-rendements d'IBOVESPA et du Dow Jones Industriel sur une base hebdomadaire entre 27/04/1993 et 03/11/2008.

This article includes results of the study of concentration of land ownership in Colombia. Initially, theoretical aspects are considered related to the Lorenz curve and Gini coefficient computation. Then, a descriptive analysis of the concentration of land ownership, establishing the relationship between owners percentages and percentage of accumulated land. Finally, we present the Gini results by region and department for the year 2000. Este artículo incluye resultados del estudio de la concentración dela tierra en Colombia. Inicialmente, se consideran aspectos teóricosrelacionados con la curva de Lorenz y el cálculo del Gini. Luego, sehace un análisis descriptivo de la concentración de la tierra,estableciendo la relación entre porcentajes de propietarios yporcentaje de tierra acumulada. Finalmente, se presentan losresultados del Gini, por regiones y por departamentos, para el año2000.

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.