Seleção de covariância para o modelo grafo gaussiano via reversible jump

Abstract

The purpose of the Graphical Gaussian model is to find the covariance structure that represents the relationship between random variables, whose joint distribution is a multivariate normal. This is a tool used to modeling Gaussian graphs. The inference of parameters of this type of modeling is commonly based on maximum likelihood estimation. However, this type of methodology requires the adjustment of all possible models to verify which model best represents the relationship between the variables. In case any model, among all the possibilities, presents an estimation problem, the result may not represent the true relationship between the variables. We propose alterations in the procedure based on the Reversible Jump algorithm of Dobra et al. (2011) for selecting and fitting the Graphical Gaussian model. We also create indicators to evaluate simulation results from a Graphical Gaussian model. The results obtained in this work are favorable to our proposal presented, in which an improvement in the model selection method was observed, reducing the error when searching for the covariance structure.