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Bayesian marginal equivalence of elliptical regression models. (English) Zbl 0786.62044

Summary: The use of proper prior densities in regression models with multivariate nonnormal elliptical error distributions is examined when the scale matrix is known up to a precision factor \(\tau\), treated as a nuisance parameter. Marginally equivalent models preserve the convenient predictive and posterior results on the parameter of interest \(\beta\) 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 nonnormal elliptical densities representing very different patterns of tail behaviour. In a linear framework, so-called semiconjugate prior structures are defined as leading to marginal equivalence to a normal data density with a fully natural conjugate prior.

MSC:

62F15 Bayesian inference
62J99 Linear inference, regression
62P20 Applications of statistics to economics
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