Bayesian marginal equivalence of elliptical regression models

Jacek Osiewalski and Mark Steel

UC3M Working papers. Economics from Universidad Carlos III de Madrid. Departamento de Economía

Abstract: The use of proper prior densities in regression models with multivariate non-Normal elliptical error distributions is examined when the scale matrix is known up to a precision factor T, treated as a nuisance parameter. Marginally equivalent models preserve the convenient predictive and posterior results on the parameter of interest B obtained in the reference case of the Normal model and its conditionally natural conjugate gamma prior. Prior densities inducing this property are derived for two special cases of non-Normal elliptical densities representing very different patterns of tail behavior. In a linear framework, so-called semi-conjugate prior structures are defined as leading to marginal equivalence to a Normal data density with a fully natural conjugate prior.

Keywords: Multivariate; elliptical; data; densities; Proper; priors; Model; robustness; Student; t; density (search for similar items in EconPapers)
Date: 1992-02
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Related works:
Journal Article: Bayesian marginal equivalence of elliptical regression models (1993)
Working Paper: Bayesian Marginal Equivalence of Elliptical Regression Models (1991)
Working Paper: Bayesian marginal equivalence of elliptical regression models (1991)
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Persistent link: https://EconPapers.repec.org/RePEc:cte:werepe:10950

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