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Bayesian Regression Analysis with scale mixtures of normals

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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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  • Carmen Fernandez & Mark F J Steel, 1999. "Bayesian Regression Analysis with scale mixtures of normals," ESE Discussion Papers 27, Edinburgh School of Economics, University of Edinburgh.
  • Handle: RePEc:edn:esedps:27
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    1. Eric Jacquier & Nicholas G. Polson & Peter Rossi, "undated". "Stochastic Volatility: Univariate and Multivariate Extensions," Rodney L. White Center for Financial Research Working Papers 19-95, Wharton School Rodney L. White Center for Financial Research.
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    6. Fernandez, Carmen & Osiewalski, Jacek & Steel, Mark F. J., 1997. "On the use of panel data in stochastic frontier models with improper priors," Journal of Econometrics, Elsevier, vol. 79(1), pages 169-193, July.
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    1. 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.
    2. 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.
    3. Fernandez, Carmen & Koop, Gary & Steel, Mark, 2000. "A Bayesian analysis of multiple-output production frontiers," Journal of Econometrics, Elsevier, vol. 98(1), pages 47-79, September.
    4. Fengkai Yang & Haijing Yuan, 2017. "A Non-iterative Bayesian Sampling Algorithm for Linear Regression Models with Scale Mixtures of Normal Distributions," Computational Economics, Springer;Society for Computational Economics, vol. 49(4), pages 579-597, April.
    5. 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/.
    6. Jung, Yeun Ji & Hobert, James P., 2014. "Spectral properties of MCMC algorithms for Bayesian linear regression with generalized hyperbolic errors," Statistics & Probability Letters, Elsevier, vol. 95(C), pages 92-100.
    7. Gernot Doppelhofer & Melvyn Weeks, 2011. "Robust Growth Determinants," CESifo Working Paper Series 3354, CESifo Group Munich.
    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. Jose T.A.S. Ferreira & Mark F.J. Steel, 2004. "Bayesian Multivariate Regression Analysis with a New Class of Skewed Distributions," Econometrics 0403001, EconWPA.
    10. 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.
    11. 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.
    12. repec:gam:jsusta:v:9:y:2017:i:4:p:635-:d:96115 is not listed on IDEAS
    13. 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.
    14. 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.
    15. 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.

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