A generalization of Bayesian estimation in finite mixture of distributions

Abstract

Se emplea metodologa bayesiana, especficamente el muestreador de Gibbs y el algoritmo de Metropolis-Hastings, para estimar los parmetros en una mixtura finita de distribuciones pertenecientes a la familia exponencial biparamtrica, o a la familia de weibull biparamtrica, modelando media y varianza de las distribuciones involucradas. En una mixtura de k distribuciones hay m de un familia de distribuciones y k − m de otra familia de distribuciones, m = 0, . . . , k. Las distribuciones que se trabajaron en los algoritmos fueron especficamente, normal y exponencial, normal y gama, y normal y weibull. La media y la varianza se modelaron con regresiones lineales y no lineales con un nmero arbitrario de covariables. Se aplic la metodologa bayesiana a la mixtura finita para modelar ejemplos tpicos de la estadstica espacial y de los modelos TAR de series de tiempo no lineales. / Abstract. Bayesian methodology is employed, mainly the Gibbs sampler and theMetropolis- Hastings algorithm, to estimate the parameters in a finite mixture of distributions belonging to the exponential biparametric family, or the biparametric weibull family of distributions, modeling the mean and the variance of all the distributions involved. In a mixture consisting of k distributions, there are m from one family and k−m from another family, m = 0, . . . , k. The algorithms worked with distributions from the normal and exponential families, normal and gamma families, and normal and weibull families. The mean and the variance, with an arbitrary number of covariates, were modelled with linear and non linear regressions. Bayesian methodology was applied to finite mixtures to model typical examples from spatial statistics and from non linear time series TAR models.