Approximate Gibbs sampler for Bayesian Huberized lasso

The Bayesian lasso is well-known as a alternative for Lasso. Although the advantage of capable full probabilistic uncertain quantification parameters, corresponding posterior distribution can be sensitive to outliers. To overcome such problem, robust regression models have been proposed in recent years. In this paper, we consider and efficient estimation Huberized fully perspective. A new computation algorithm proposed. approximate Gibbs sampler based on approximation conditional it possible estimate tuning parameter robustness pseudo-Huber loss function. Some theoretical properties are also derived. We illustrate performance method through simulation studies real data examples.