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., 1990.
"Robust Bayesian Inference In Elliptical Regression Models,"
9032, Tilburg - 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.
- Osiewalski, J. & Steel, M.F.J., 1990. "Robust Bayesian inference in elliptical regression models," Discussion Paper 1990-32, Tilburg University, Center for Economic Research.
- Kleibergen, Frank & Paap, Richard, 2002.
"Priors, posteriors and bayes factors for a Bayesian analysis of cointegration,"
Journal of Econometrics,
Elsevier, vol. 111(2), pages 223-249, December.
- Kleibergen, F.R. & Paap, R., 1998. "Priors, posteriors and Bayes factors for a Bayesian analysis of cointegration," Econometric Institute Research Papers EI 9821, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
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