Bayesian Variations on the Frisch and Waugh Theme
The paper is devoted to discussing consequences of the so-called Frisch-Waugh Theorem to posterior inference and Bayesian model comparison. We adopt a generalised normal linear regression framework and weaken its assumptions in order to cover non-normal, jointly elliptical sampling distributions, autoregressive specifications, additional nuisance parameters and multi-equation SURE or VAR models. The main result is that inference based on the original full Bayesian model can be obtained using transformed data and reduced parameter spaces, provided the prior density for scale or precision parameters is appropriately modified.
Volume (Year): 3 (2011)
Issue (Month): 1 (March)
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- Osiewalski, J. & Steel, M.F.J., 1990.
"Robust Bayesian inference in elliptical regression models,"
1990-32, Tilburg University, Center for Economic Research.
- Osiewalski, Jacek & Steel, Mark F. J., 1993. "Robust bayesian inference in elliptical regression models," Journal of Econometrics, Elsevier, vol. 57(1-3), pages 345-363.
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"Priors, posteriors and bayes factors for a Bayesian analysis of cointegration,"
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Elsevier, vol. 111(2), pages 223-249, December.
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