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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.

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.

En este artículo, se introduce un análisis bayesiano para datos multivariados de sobrevivencia en presencia de un vector de covariables y observaciones censuradas. Diferentes “fragilidades” o variables latentes son consideradas para capturar la correlación entre los tiempos de sobrevivencia para un mismo individuo. Asumimos distribuciones Weibull o Gamma generalizadas considerando datos de tiempo de vida a derecha. Desarrollamos el análisis bayesiano usando métodos Markov Chain Monte Carlo (MCMC). In this paper, we introduce a Bayesian analysis for survival multivariate data in the presence of a covariate vector and censored observations. Different “frailties” or latent variables are considered to capture the correlation among the survival times for the same individual. We assumeWeibull or generalized Gamma distributions considering right censored lifetime data. We develop the Bayesian analysis using Markov Chain Monte Carlo (MCMC) methods.

In this paper, we compare the performance of two statistical approaches for the analysis of data obtained from the social research area. In the first approach, we use normal models with joint regression modelling for the mean and for the variance heterogeneity. In the second approach, we use hierarchical models. In the first case, individual and social variables are included in the regression modelling for the mean and for the variance, as explanatory variables, while in the second case, the variance at level 1 of the hierarchical model depends on the individuals (age of the individuals), and in the level 2 of the hierarchical model, the variance is assumed to change according to socioeconomic stratum. Applying these methodologies, we analyze a Colombian tallness data set to find differences that can be explained by socioeconomic conditions. We also present some theoretical and empirical results concerning the two models. From this comparative study, we conclude that it is better to jointly modelling the mean and variance heterogeneity in all cases. We also observe that the convergence of the Gibbs sampling chain used in the Markov Chain Monte Carlo method for the jointly modeling the mean and variance heterogeneity is quickly achieved. En este artículo, comparamos el desempeño de dos aproximaciones estadísticas para el análisis de datos obtenidos en el área de investigación social. En la primera, utilizamos modelos normales con modelación conjunta de media y de heterogeneidad de varianza. En la segunda, utilizamos modelos jerárquicos. En el primer caso, se incluyen variables del individuo y de su entorno social en los modelos de media y varianza, como variables explicativas, mientras que, en el segundo, la variación en nivel 1 del modelo jerárquico depende de los individuos (edad de los individuos). En el nivel 2 del modelo jerárquico, se asume que la variación depende del estrato socioeconómico. Aplicando estas metodologías, analizamos un conjunto de datos de talla de los colombianos, para encontrar diferencias que pueden explicarse por sus condiciones socioeconómicas. También presentamos resultados teóricos y empíricos relacionados con los dos modelos considerados. A partir de este estudio comparativo concluimos que, en todos los casos, es "mejor" la modelación conjunta de media y varianza. Además de una interpretación muy sencilla, observamos una rápida convergencia de las cadenas generadas con la metodología propuesta para el ajuste de estos modelos.