论文标题
贝叶斯Huberized Lasso的近似Gibbs采样器
Approximate Gibbs sampler for Bayesian Huberized lasso
论文作者
论文摘要
贝叶斯套索以拉索的贝叶斯替代品而闻名。尽管贝叶斯套索的优势能够完全概率不确定参数，但相应的后验分布可能对异常值敏感。为了克服此类问题，近年来已经提出了强大的贝叶斯回归模型。在本文中，我们考虑了完全贝叶斯观点的贝叶斯huberized Lasso回归的强大和有效估计。提出了一种新的后验计算算法，用于贝叶斯huberized Lasso回归。提出的近似Gibbs采样器基于完全条件分布的近似值，并且可以估算一个调谐参数，以实现伪Huber损失函数的鲁棒性。也得出了后验分布的一些理论特性。我们通过模拟研究和实际数据示例说明了所提出的方法的性能。
The Bayesian lasso is well-known as a Bayesian alternative for Lasso. Although the advantage of the Bayesian lasso is capable of full probabilistic uncertain quantification for parameters, the corresponding posterior distribution can be sensitive to outliers. To overcome such problem, robust Bayesian regression models have been proposed in recent years. In this paper, we consider the robust and efficient estimation for the Bayesian Huberized lasso regression in fully Bayesian perspective. A new posterior computation algorithm for the Bayesian Huberized lasso regression is proposed. The proposed approximate Gibbs sampler is based on the approximation of full conditional distribution and it is possible to estimate a tuning parameter for robustness of the pseudo-Huber loss function. Some theoretical properties of the posterior distribution are also derived. We illustrate performance of the proposed method through simulation studies and real data examples.
