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2020•Bayesian AnalysisOpen access

Objective Bayesian Analysis for the Student-t Linear Regression

Daojiang He, Dongchu Sun, Lei He

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Abstract

In this paper, objective Bayesian analysis for the Student-t linear regression model with unknown degrees of freedom is studied. The reference priors under all the possible group orderings for the parameters in the model are derived. The posterior propriety under each reference prior is validated by considering a larger class of priors. Simulation studies are carried out to investigate the frequentist properties of Bayesian estimators based on the reference priors. Finally, the Bayesian approach is applied to two real data sets.

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What this paper is about

In this paper, objective Bayesian analysis for the Student-t linear regression model with unknown degrees of freedom is studied. The reference priors under all the possible group orderings for the parameters in the model are derived. The posterior propriety under each reference prior is validated by considering a larger class of priors. Simulation studies are carried out to investigate the frequentist properties of Bayesian estimators based on the reference priors. Finally, the Bayesian approach is applied to two real data sets.

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Available abstract

In this paper, objective Bayesian analysis for the Student-t linear regression model with unknown degrees of freedom is studied. The reference priors under all the possible group orderings for the parameters in the model are derived. The posterior propriety under each reference prior is validated by considering a larger class of priors. Simulation studies are carried out to investigate the frequentist properties of Bayesian estimators based on the reference priors. Finally, the Bayesian approach is applied to two real data sets.

Key concepts: Prior probability, Frequentist inference, Bayesian linear regression, Bayesian probability, Bayesian multivariate linear regression, Linear regression, Mathematics, Regression analysis

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