Robust Bayesian Regression with Synthetic Posterior Distributions
Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not necessarily straightforward. We here propose a Bayesian approac...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-06-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/22/6/661 |
| _version_ | 1827715053930938368 |
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| author | Shintaro Hashimoto Shonosuke Sugasawa |
| author_facet | Shintaro Hashimoto Shonosuke Sugasawa |
| author_sort | Shintaro Hashimoto |
| collection | DOAJ |
| description | Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not necessarily straightforward. We here propose a Bayesian approach to robust inference on linear regression models using synthetic posterior distributions based on <i>γ</i>-divergence, which enables us to naturally assess the uncertainty of the estimation through the posterior distribution. We also consider the use of shrinkage priors for the regression coefficients to carry out robust Bayesian variable selection and estimation simultaneously. We develop an efficient posterior computation algorithm by adopting the Bayesian bootstrap within Gibbs sampling. The performance of the proposed method is illustrated through simulation studies and applications to famous datasets. |
| first_indexed | 2024-03-10T19:10:11Z |
| format | Article |
| id | doaj.art-6e4f9a03860148c6a994676c55dfd0e9 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T19:10:11Z |
| publishDate | 2020-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-6e4f9a03860148c6a994676c55dfd0e92023-11-20T03:53:01ZengMDPI AGEntropy1099-43002020-06-0122666110.3390/e22060661Robust Bayesian Regression with Synthetic Posterior DistributionsShintaro Hashimoto0Shonosuke Sugasawa1Department of Mathematics, Hiroshima University, Hiroshima 739-8521, JapanCenter for Spatial Information Science, The University of Tokyo, Chiba 277-8568, JapanAlthough linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not necessarily straightforward. We here propose a Bayesian approach to robust inference on linear regression models using synthetic posterior distributions based on <i>γ</i>-divergence, which enables us to naturally assess the uncertainty of the estimation through the posterior distribution. We also consider the use of shrinkage priors for the regression coefficients to carry out robust Bayesian variable selection and estimation simultaneously. We develop an efficient posterior computation algorithm by adopting the Bayesian bootstrap within Gibbs sampling. The performance of the proposed method is illustrated through simulation studies and applications to famous datasets.https://www.mdpi.com/1099-4300/22/6/661Bayesian bootstrapBayesian lassodivergenceGibbs samplinglinear regression |
| spellingShingle | Shintaro Hashimoto Shonosuke Sugasawa Robust Bayesian Regression with Synthetic Posterior Distributions Entropy Bayesian bootstrap Bayesian lasso divergence Gibbs sampling linear regression |
| title | Robust Bayesian Regression with Synthetic Posterior Distributions |
| title_full | Robust Bayesian Regression with Synthetic Posterior Distributions |
| title_fullStr | Robust Bayesian Regression with Synthetic Posterior Distributions |
| title_full_unstemmed | Robust Bayesian Regression with Synthetic Posterior Distributions |
| title_short | Robust Bayesian Regression with Synthetic Posterior Distributions |
| title_sort | robust bayesian regression with synthetic posterior distributions |
| topic | Bayesian bootstrap Bayesian lasso divergence Gibbs sampling linear regression |
| url | https://www.mdpi.com/1099-4300/22/6/661 |
| work_keys_str_mv | AT shintarohashimoto robustbayesianregressionwithsyntheticposteriordistributions AT shonosukesugasawa robustbayesianregressionwithsyntheticposteriordistributions |