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Objective Bayesian analysis for the Student-t regression model

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  • Thaís C. O. Fonseca
  • Marco A. R. Ferreira
  • Helio S. Migon

Abstract

We develop a Bayesian analysis based on two different Jeffreys priors for the Student-t regression model with unknown degrees of freedom. It is typically difficult to estimate the number of degrees of freedom: improper prior distributions may lead to improper posterior distributions, whereas proper prior distributions may dominate the analysis. We show that Bayesian analysis with either of the two considered Jeffreys priors provides a proper posterior distribution. Finally, we show that Bayesian estimators based on Jeffreys analysis compare favourably to other Bayesian estimators based on priors previously proposed in the literature. Copyright 2008, Oxford University Press.

Suggested Citation

  • Thaís C. O. Fonseca & Marco A. R. Ferreira & Helio S. Migon, 2008. "Objective Bayesian analysis for the Student-t regression model," Biometrika, Biometrika Trust, vol. 95(2), pages 325-333.
    • Handle: RePEc:oup:biomet:v:95:y:2008:i:2:p:325-333
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    Cited by:

    1. Rubio, F.J. & Steel, M.F.J., 2011. "Inference for grouped data with a truncated skew-Laplace distribution," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3218-3231, December.
    2. Abanto-Valle, Carlos A. & Dey, Dipak K., 2014. "State space mixed models for binary responses with scale mixture of normal distributions links," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 274-287.
    3. Gang Cheng & Sicong Wang & Yuhong Yang, 2015. "Forecast Combination under Heavy-Tailed Errors," Econometrics, MDPI, vol. 3(4), pages 1-28, November.
    4. Ricardo S. Ehlers, 2011. "Comparison of Bayesian models for production efficiency," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(11), pages 2433-2443, January.
    5. Victor H. Lachos & Celso R.B. Cabral & Carlos A. Abanto-Valle, 2012. "A non-iterative sampling Bayesian method for linear mixed models with normal independent distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(3), pages 531-549, July.
    6. Filidor Vilca & Caio L. N. Azevedo & N. Balakrishnan, 2017. "Bayesian inference for sinh-normal/independent nonlinear regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(11), pages 2052-2074, August.
    7. Antonio Parisi & B. Liseo, 2018. "Objective Bayesian analysis for the multivariate skew-t model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(2), pages 277-295, June.
    8. Aparecida Souza & Helio Migon, 2010. "Bayesian outlier analysis in binary regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(8), pages 1355-1368.
    9. Villa, Cristiano & Rubio, Francisco J., 2018. "Objective priors for the number of degrees of freedom of a multivariate t distribution and the t-copula," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 197-219.
    10. Aldo M. Garay & Heleno Bolfarine & Victor H. Lachos & Celso R.B. Cabral, 2015. "Bayesian analysis of censored linear regression models with scale mixtures of normal distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(12), pages 2694-2714, December.
    11. Debdeep Pati & David Dunson, 2014. "Bayesian nonparametric regression with varying residual density," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(1), pages 1-31, February.
    12. Christian E. Galarza & Tsung-I Lin & Wan-Lun Wang & Víctor H. Lachos, 2021. "On moments of folded and truncated multivariate Student-t distributions based on recurrence relations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(6), pages 825-850, August.
    13. C. A. Abanto-Valle & V. H. Lachos & Dipak K. Dey, 2015. "Bayesian Estimation of a Skew-Student-t Stochastic Volatility Model," Methodology and Computing in Applied Probability, Springer, vol. 17(3), pages 721-738, September.
    14. Hedibert F. Lopes & Nicholas G. Polson, 2016. "Particle Learning for Fat-Tailed Distributions," Econometric Reviews, Taylor & Francis Journals, vol. 35(8-10), pages 1666-1691, December.
    15. Cristiano C. Santos & Rosangela H. Loschi, 2017. "Maximum likelihood estimation and parameter interpretation in elliptical mixed logistic regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 209-230, March.
    16. Moreno Bevilacqua & Christian Caamaño‐Carrillo & Reinaldo B. Arellano‐Valle & Víctor Morales‐Oñate, 2021. "Non‐Gaussian geostatistical modeling using (skew) t processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 212-245, March.
    17. Pianto, Donald M. & Cribari-Neto, Francisco, 2011. "Dealing with monotone likelihood in a model for speckled data," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1394-1409, March.
    18. Ferreira, Marco A.R. & Porter, Erica M. & Franck, Christopher T., 2021. "Fast and scalable computations for Gaussian hierarchical models with intrinsic conditional autoregressive spatial random effects," Computational Statistics & Data Analysis, Elsevier, vol. 162(C).
    19. Shuaimin Kang & Guangying Liu & Howard Qi & Min Wang, 2018. "Bayesian Variance Changepoint Detection in Linear Models with Symmetric Heavy-Tailed Errors," Computational Economics, Springer;Society for Computational Economics, vol. 52(2), pages 459-477, August.
    20. Gagnon, Philippe & Hayashi, Yoshiko, 2023. "Theoretical properties of Bayesian Student-t linear regression," Statistics & Probability Letters, Elsevier, vol. 193(C).
    21. Wang, Min & Yang, Mingan, 2016. "Posterior property of Student-t linear regression model using objective priors," Statistics & Probability Letters, Elsevier, vol. 113(C), pages 23-29.
    22. Alain Hecq & Sean Telg & Lenard Lieb, 2017. "Do Seasonal Adjustments Induce Noncausal Dynamics in Inflation Rates?," Econometrics, MDPI, vol. 5(4), pages 1-22, October.
    23. Zellner, Arnold & Ando, Tomohiro, 2010. "Bayesian and non-Bayesian analysis of the seemingly unrelated regression model with Student-t errors, and its application for forecasting," International Journal of Forecasting, Elsevier, vol. 26(2), pages 413-434, April.

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