Bayesian Regression Analysis With Scale Mixtures Of Normals
AbstractThis paper considers a Bayesian analysis of the linear regression model under independent sampling from general scale mixtures of normals. Using a common reference prior, we investigate the validity of Bayesian inference and the existence of posterior moments of the regression and scale parameters. We find that whereas existence of the posterior distribution does not depend on the choice of the design matrix or the mixing distribution, both of them can crucially intervene in the existence of posterior moments. We identify some useful characteristics that allow for an easy verification of the existence of a wide range of moments. In addition, we provide full characterizations under sampling from finite mixtures of normals, Pearson VII, or certain modulated normal distributions. For empirical applications, a numerical implementation based on the Gibbs sampler is recommended.
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Bibliographic InfoArticle provided by Cambridge University Press in its journal Econometric Theory.
Volume (Year): 16 (2000)
Issue (Month): 01 (February)
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Other versions of this item:
- Carmen Fernandez & Mark F. J. Steel, 2004. "Bayesian Regression Analysis with scale mixtures of normals," ESE Discussion Papers 27, Edinburgh School of Economics, University of Edinburgh.
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- Juarez, Miguel A. & Steel, Mark F. J., 2006. "Model-based Clustering of non-Gaussian Panel Data," MPRA Paper 880, University Library of Munich, Germany.
- Doppelhofer, Gernot & Weeks, Melvyn, 2011.
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"Non-Gaussian dynamic Bayesian modelling for panel data,"
450, University Library of Munich, Germany.
- Miguel A. Juárez & Mark F. J. Steel, 2010. "Non‐gaussian dynamic bayesian modelling for panel data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(7), pages 1128-1154, November/.
- De la Cruz, Rolando, 2008. "Bayesian non-linear regression models with skew-elliptical errors: Applications to the classification of longitudinal profiles," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 436-449, December.
- Abanto-Valle, C.A. & Bandyopadhyay, D. & Lachos, V.H. & Enriquez, I., 2010. "Robust Bayesian analysis of heavy-tailed stochastic volatility models using scale mixtures of normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 2883-2898, December.
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- Ley, Eduardo & Steel, Mark F.J., 2012. "Mixtures of g-priors for Bayesian model averaging with economic applications," Journal of Econometrics, Elsevier, vol. 171(2), pages 251-266.
- Eduardo Ley & Mark F.J. Steel, 2011. "Mixtures of g-priors for bayesian model averaging with economic applications," Statistics and Econometrics Working Papers ws112116, Universidad Carlos III, Departamento de Estadística y Econometría.
- Ley, Eduardo & Steel, Mark F.J., 2011. "Mixtures of g-priors for Bayesian Model Averaging with economic application," Policy Research Working Paper Series 5732, The World Bank.
- Ley, Eduardo & Steel, Mark F. J., 2010. "Mixtures of g-priors for Bayesian model averaging with economic applications," MPRA Paper 26941, University Library of Munich, Germany.
- Jose T.A.S. Ferreira & Mark F.J. Steel, 2004. "Bayesian Multivariate Regression Analysis with a New Class of Skewed Distributions," Econometrics 0403001, EconWPA.
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