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Biometrika Advance Access originally published online on April 25, 2008
Biometrika 2008 95(2):325-333; doi:10.1093/biomet/asn001
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© 2008 Biometrika Trust

Articles

Objective Bayesian analysis for the Student-t regression model

Thaís C. O. Fonseca

Department of Statistics, University of Warwick, Coventry CV4 7AL, U.K. T.C.O.Fonseca{at}warwick.ac.uk

Marco A. R. Ferreira

Department of Statistics, University of Missouri, Columbia, Missouri 65211-6100, U.S.A. ferreiram{at}missouri.edu

Helio S. Migon

Department of Statistics, Federal University of Rio de Janeiro, CEP: 21945-970, Brazil migon{at}im.ufrj.br

Received for publication 1 May 2006. Revision received 1 November 2007.
  Abstract

We develop a Bayesian analysis based on two different Jeffreys priors for the Student-t regression model with unknown degrees of freedom. It is typically difficult to estimate the number of degrees of freedom: improper prior distributions may lead to improper posterior distributions, whereas proper prior distributions may dominate the analysis. We show that Bayesian analysis with either of the two considered Jeffreys priors provides a proper posterior distribution. Finally, we show that Bayesian estimators based on Jeffreys analysis compare favourably to other Bayesian estimators based on priors previously proposed in the literature.

Key Words: Heavy tail behaviour • Jeffreys prior • Robustness to outliers


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