Bayesian Regression Analysis with scale mixtures of normals

Carmen Fernandez and Mark Steel

Edinburgh School of Economics Discussion Paper Series from Edinburgh School of Economics, University of Edinburgh

Abstract: This paper considers a Bayesian analysis of the linear regression model under independent sampling from general scale mixtures of Normals. Using a common reference prior, we investigate the validity of Bayesian inference and the existence of posterior moments of the regression and scale parameters. We find that whereas existence of the posterior distribution does not depend on the choice of the design matrix or the mixing distribution, both of them can crucially intervene in the existence of posterior moments. We identify some useful characteristics that allow for an easy verification of the existence of a wide range of moments. In addition, we provide full characterizations under sampling from finite mixtures of Normals, Pearson VII or certain Modulated Normal distributions. For empirical applications, a numerical implementation based on the Gibbs sampler is recommended.

Pages: 32
Date: 1999
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Citations: View citations in EconPapers (2)

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Related works:
Journal Article: BAYESIAN REGRESSION ANALYSIS WITH SCALE MIXTURES OF NORMALS (2000)
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Persistent link: https://EconPapers.repec.org/RePEc:edn:esedps:27

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