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.

翻译：Bayesian lasso 是一个众所周知的Lasso的Bayesian替代物。 虽然Bayesian lasso的优势能够对参数进行完全概率不确定的量化, 但相应的后方分布对外部分布可能十分敏感。 为了克服这些问题,近年来提出了强有力的Bayesian回归模型。 在本文中,我们从完全Bayesian的角度考虑对Bayesian Huberized lasso 回归的可靠和高效估算。 提出了Bayesian Huberized lasso回归的新的后方计算算法。 拟议的近似Gibbs取样器以完全有条件分布的近似值为基础, 并且有可能估算出一个对伪Huber 损耗函数的稳健性的调控参数。 后方分布的一些理论特性也得到推导出。 我们通过模拟研究和真实数据实例来说明拟议方法的绩效。