Wednesday, May 30, 2007

Objective Bayesian analysis for the Student-t regression model

Marco Ferreira
(University of Missouri-Columbia)

Abstract: We develop Bayesian analysis based on the Jeffreys prior for the Student-t regression model with unknown degrees of freedom. This is of great practical interest, since economic and financial datasets often exhibit heavy tail behavior and models with Student-t errors can accommodate outliers. Unfortunately, the estimation of the number of degrees of freedom is not straightforward: maximum likelihood estimation is problematic, improper prior distributions may lead to improper posterior distributions, and proper prior distributions previously proposed in the literature may strongly influence the analysis. As an alternative, we derive the Jeffreys-rule prior and the independence Jeffreys prior for the Student-t regression model with unknown degrees of freedom, develop Bayesian estimation using Markov chain Monte Carlo and Bayesian model selection with fractional Bayes factors. We show that Bayesian analysis with either of these two Jeffreys priors provides a proper posterior distribution. Moreover, through an extensive Monte Carlo study, we show that Bayesian estimators based on Jeffreys analysis compare favorably to other Bayesian estimators based on priors previously proposed in the literature. Finally, we illustrate the use of our proposed approach with the analysis of the well known dataset on per capita income and spending in public schools in the United States.

Wednesday, May 30, 2007
Time: 15h00
Room: Sala Delta, Edificio Quelhas, ISEG