Park and Casella (2008) provided the Bayesian lasso for linear models by assigning scale mixture of normal (SMN) priors on the parameters and independent exponential priors on their variances. In this paper, we propose an alternative Bayesian analysis of the lasso problem. A different hierarchical formulation of Bayesian lasso is introduced by utilizing the scale mixture of uniform (SMU) representation of the Laplace density. We consider a fully Bayesian treatment that leads to a new Gibbs sampler with tractable full conditional posterior distributions. Empirical results and real data analyses show that the new algorithm has good mixing property and performs comparably to the existing Bayesian method in terms of both prediction accuracy and variable selection. An ECM algorithm is provided to compute the MAP estimates of the parameters. Easy extension to general models is also briefly discussed.

中文翻译：

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 新的贝叶斯套索


Park 和 Casella（2008）通过在参数上分配正态（SMN）先验的尺度混合和在其方差上分配独立指数先验，为线性模型提供了贝叶斯套索。在本文中，我们提出了套索问题的另一种贝叶斯分析。通过利用拉普拉斯密度的均匀尺度混合 (SMU) 表示，引入了贝叶斯套索的不同层次公式。我们考虑采用完全贝叶斯处理，产生具有易处理的完全条件后验分布的新吉布斯采样器。实证结果和真实数据分析表明，新算法具有良好的混合特性，在预测精度和变量选择方面与现有贝叶斯方法相当。提供 ECM 算法来计算参数的 MAP 估计。还简要讨论了对通用模型的简单扩展。