Gibbs sampling method for the Bayesian adaptive elastic net |
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Authors: | Ali Aghamohammadi M R Meshkani |
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Institution: | 1. Department of Statistics, University of Zanjan, Zanjan, Iran;2. Department of Statistics, Shahid Beheshti University, Tehran, Iran |
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Abstract: | This article considers the adaptive elastic net estimator for regularized mean regression from a Bayesian perspective. Representing the Laplace distribution as a mixture of Bartlett–Fejer kernels with a Gamma mixing density, a Gibbs sampling algorithm for the adaptive elastic net is developed. By introducing slice variables, it is shown that the mixture representation provides a Gibbs sampler that can be accomplished by sampling from either truncated normal or truncated Gamma distribution. The proposed method is illustrated using several simulation studies and analyzing a real dataset. Both simulation studies and real data analysis indicate that the proposed approach performs well. |
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Keywords: | Bayesian mean regression Elastic net Gibbs sampler Hierarchical model Mixture of Bartlett–Fejer kernels |
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