Estimación bayesiana de modelos lineales generalizados en datos funcionales

Abstract

Current studies, should not always be handled as usual data where an individual represents a specific object, if not as functional data, such that an individual represents a curve, in which its continuous nature is conserved and a significant reduction of the dimension of the data. Functional variables are characterized by the evolution of a variable over time (stochastic process), so that the values they take are, in general, functions of one or several arguments instead of vectors as in classical multivariate analysis. (Master course in statistics, University of Granada, 2016). Within the analysis of functional data, generalized linear models are addressed; these models group both models with numerical and categorical variables, which leads us to take into account other distributions (Poisson, binomial, hypergeometric, gamma, multinomial, etc.), in addition to the normal one, and these advances in the theory of linear models are drunk to Nelder and Wedderbum, and jointly Bayes’s theorem is imposed, which transcends classical application, especially when it is extended to another context in which probability is not exclusively understood as the relative frequency of an event long term, but as the degree of personal conviction that the event occurs or may occur (subjective definition of probability). By admitting a subjective management of probability, the Bayesian analyst will be able to make probability judgments about a H hypothesis and express in this way his degree of conviction in this regard, both before and after having observed the data ([PDF] Bayesian Statistics). Considering these topics, a study of Latin America (Without Suriname and Guyana) of the democracy index EIU is made, based on three indices, which are: Per cápita Gross Domestic Product and GINI Index from the year 2002 until 2015.