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Robust Bayesian seemingly unrelated regression model

Chamberlain Mbah (UGent) , Kris Peremans, Stefan Van Aelst and Dries Benoit (UGent)
(2019) COMPUTATIONAL STATISTICS. 34(3). p.1135-1157
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Abstract
A robust Bayesian model for seemingly unrelated regression is proposed. By using heavy-tailed distributions for the likelihood, robustness in the response variable is attained. In addition, this robust procedure is combined with a diagnostic approach to identify observations that are far from the bulk of the data in the multivariate space spanned by all variables. The most distant observations are downweighted to reduce the effect of leverage points. The resulting robust Bayesian model can be interpreted as a heteroscedastic seemingly unrelated regression model. Robust Bayesian estimates are obtained by a Markov Chain Monte Carlo approach. Complications by using a heavy-tailed error distribution are resolved efficiently by representing these distributions as a scale mixture of normal distributions. Monte Carlo simulation experiments confirm that the proposed model outperforms its traditional Bayesian counterpart when the data are contaminated in the response and/or the input variables. The method is demonstrated on a real dataset.
Keywords
Statistics, Probability and Uncertainty, Statistics and Probability, Computational Mathematics, Conjugate prior, Diagnostic procedure, Heavy-tailed distributions, Markov Chain Monte Carlo, Robustness, Scale mixture of normal distributions, DIRECT MONTE-CARLO, SENSITIVITY, INFERENCE

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Citation

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Chicago
Mbah, Chamberlain, Kris Peremans, Stefan Van Aelst, and Dries Benoit. 2019. “Robust Bayesian Seemingly Unrelated Regression Model.” Computational Statistics 34 (3): 1135–1157.
APA
Mbah, C., Peremans, K., Van Aelst, S., & Benoit, D. (2019). Robust Bayesian seemingly unrelated regression model. COMPUTATIONAL STATISTICS, 34(3), 1135–1157.
Vancouver
1.
Mbah C, Peremans K, Van Aelst S, Benoit D. Robust Bayesian seemingly unrelated regression model. COMPUTATIONAL STATISTICS. Springer; 2019;34(3):1135–57.
MLA
Mbah, Chamberlain et al. “Robust Bayesian Seemingly Unrelated Regression Model.” COMPUTATIONAL STATISTICS 34.3 (2019): 1135–1157. Print.
@article{8583790,
  abstract     = {A robust Bayesian model for seemingly unrelated regression is proposed. By using heavy-tailed distributions for the likelihood, robustness in the response variable is attained. In addition, this robust procedure is combined with a diagnostic approach to identify observations that are far from the bulk of the data in the multivariate space spanned by all variables. The most distant observations are downweighted to reduce the effect of leverage points. The resulting robust Bayesian model can be interpreted as a heteroscedastic seemingly unrelated regression model. Robust Bayesian estimates are obtained by a Markov Chain Monte Carlo approach. Complications by using a heavy-tailed error distribution are resolved efficiently by representing these distributions as a scale mixture of normal distributions. Monte Carlo simulation experiments confirm that the proposed model outperforms its traditional Bayesian counterpart when the data are contaminated in the response and/or the input variables. The method is demonstrated on a real dataset.},
  author       = {Mbah, Chamberlain and Peremans, Kris and Van Aelst, Stefan and Benoit, Dries},
  issn         = {0943-4062},
  journal      = {COMPUTATIONAL STATISTICS},
  keywords     = {Statistics,Probability and Uncertainty,Statistics and Probability,Computational Mathematics,Conjugate prior,Diagnostic procedure,Heavy-tailed distributions,Markov Chain Monte Carlo,Robustness,Scale mixture of normal distributions,DIRECT MONTE-CARLO,SENSITIVITY,INFERENCE},
  language     = {eng},
  number       = {3},
  pages        = {1135--1157},
  publisher    = {Springer},
  title        = {Robust Bayesian seemingly unrelated regression model},
  url          = {http://dx.doi.org/10.1007/s00180-018-0854-3},
  volume       = {34},
  year         = {2019},
}
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