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Bayesian Regression Analysis with scale mixtures of normals

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  • Carmen Fernandez
  • Mark F. J. Steel

Abstract

This 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 Info

Paper provided by Edinburgh School of Economics, University of Edinburgh in its series ESE Discussion Papers with number 27.

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Date of creation: May 2004
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Handle: RePEc:edn:esedps:27

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Cited by:
  1. 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.
  2. 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.
  3. 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/.
  4. Jose T.A.S. Ferreira & Mark F.J. Steel, 2004. "Bayesian Multivariate Regression Analysis with a New Class of Skewed Distributions," Econometrics 0403001, EconWPA.
  5. Doppelhofer, Gernot & Weeks, Melvyn, 2011. "Robust Growth Determinants," Discussion Paper Series in Economics 3/2011, Department of Economics, Norwegian School of Economics.
  6. Rubio, Francisco Javier & Steel, Mark F. J., 2014. "Bayesian modelling of skewness and kurtosis with two-piece scale and shape transformations," MPRA Paper 57102, University Library of Munich, Germany.
  7. Vilca, Filidor & Balakrishnan, N. & Zeller, Camila Borelli, 2014. "A robust extension of the bivariate Birnbaum–Saunders distribution and associated inference," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 418-435.
  8. Juarez, Miguel A. & Steel, Mark F. J., 2006. "Model-based Clustering of non-Gaussian Panel Data," MPRA Paper 880, University Library of Munich, Germany.
  9. Carmen Fernandez & Gary Koop & M. F. J. Steel, 2004. "A Bayesian analysis of multiple-output production frontiers," ESE Discussion Papers 21, Edinburgh School of Economics, University of Edinburgh.
  10. Salas-Gonzalez, Diego & Kuruoglu, Ercan E. & Ruiz, Diego P., 2009. "A heavy-tailed empirical Bayes method for replicated microarray data," Computational Statistics & Data Analysis, Elsevier, vol. 53(5), pages 1535-1546, March.
  11. Rubio, Francisco Javier & Liseo, Brunero, 2014. "On the independence Jeffreys prior for skew-symmetric models," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 91-97.
  12. 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.

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