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Bayesian likelihood robustness in linear models |
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| Authors: | Daniel Peña Ruben Zamar Guohua Yan |
| Institution: | 1. Departamento de Estadistica, Facultad de Ciencias Sociales, Universidad Carlos III de Madrid, Madrid 126, Getafe 28903, Spain;2. Department of Statistics, University of British Columbia, 333-6356 Agricultural Road, Vancouver, British Columbia, Canada V6T 1Z2;3. Department of Mathematics and Statistics, University of New Brunswick, Fredericton, New Brunswick, Canada E3B 5A3 |
| Abstract: | This paper deals with the problem of robustness of Bayesian regression with respect to the data. We first give a formal definition of Bayesian robustness to data contamination, prove that robustness according to the definition cannot be obtained by using heavy-tailed error distributions in linear regression models and propose a heteroscedastic approach to achieve the desired Bayesian robustness. |
| Keywords: | Bayesian inference Heteroscedasticity Kullback&ndash Leibler divergence Robust regression |
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