Bayesian marginal equivalence of elliptical regression models
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.
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- Chib, Siddhartha & Tiwari, Ram C. & Jammalamadaka, S. Rao, 1988. "Bayes prediction in regressions with elliptical errors," Journal of Econometrics, Elsevier, vol. 38(3), pages 349-360, July.
- Jammalamadaka, S. Rao & Tiwari, Ram C. & Chib, Siddhartha, 1987. "Bayes prediction in the linear model with spherically symmetric errors," Economics Letters, Elsevier, vol. 24(1), pages 39-44.
- Osiewalski, Jacek, 1991.
"A note on Bayesian inference in a regression model with elliptical errors,"
Journal of Econometrics,
Elsevier, vol. 48(1-2), pages 183-193.
- Osiewalski, J., 1989. "A Note On Bayesian Inference In A Regression Model With Elliptical Errors," CORE Discussion Papers 1989040, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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