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A Non-iterative Bayesian Sampling Algorithm for Linear Regression Models with Scale Mixtures of Normal Distributions

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  • Fengkai Yang

    (Shandong University
    Shandong University)

  • Haijing Yuan

    (Shandong University
    Shandong University)

Abstract

The scale mixtures of Normal distributions are used as a robust alternative to the normal distribution in linear regression modelling, and a non-iterative Bayesian sampling algorithm is developed to obtain independently and identically distributed samples approximately from the observed posterior distributions, which eliminates the convergence problems in iterative Gibbs sampling. Model selection and influential analysis are conducted to choose the best fitted model and to detect the latent outliers. The performances of the methodologies are illustrated through several simulation studies by comparison with the Normal regression and Gibbs sampling, and finally, the US treasury bond prices data is analyzed using the proposed algorithm.

Suggested Citation

  • 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.
    • Handle: RePEc:kap:compec:v:49:y:2017:i:4:d:10.1007_s10614-016-9580-5
    DOI: 10.1007/s10614-016-9580-5
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    References listed on IDEAS

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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. G. J. M. Rosa & D. Gianola & C. R. Padovani, 2004. "Bayesian Longitudinal Data Analysis with Mixed Models and Thick-tailed Distributions using MCMC," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(7), pages 855-873.
    3. Fernández, Carmen & Steel, Mark F.J., 2000. "Bayesian Regression Analysis With Scale Mixtures Of Normals," Econometric Theory, Cambridge University Press, vol. 16(1), pages 80-101, February.
    4. 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.
    5. 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.
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    Cited by:

    1. Ang Shan & Fengkai Yang, 2021. "Bayesian Inference for Finite Mixture Regression Model Based on Non-Iterative Algorithm," Mathematics, MDPI, vol. 9(6), pages 1-13, March.

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