59 research outputs found
Robust Bayesian Regression with Synthetic Posterior
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 -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.Comment: 23 pages, 5 figure
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