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Bayesian Marginal Equivalence of Elliptical Regression Models

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  • Osiewalski, J.
  • Steel, M.

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.
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Suggested Citation

  • Osiewalski, J. & Steel, M., 1991. "Bayesian Marginal Equivalence of Elliptical Regression Models," Papers 9119, Tilburg - Center for Economic Research.
    • Handle: RePEc:fth:tilbur:9119
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    2. Jacek Osiewalski, 2011. "Bayesian Variations on the Frisch and Waugh Theme," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 3(1), pages 39-47, March.
    3. Arellano-Valle, R.B. & del Pino, G. & Iglesias, P., 2006. "Bayesian inference in spherical linear models: robustness and conjugate analysis," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 179-197, January.

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