标题： Lasso分布：性质、抽样方法及在贝叶斯Lasso回归中的应用 显示英文标题

标题： The Lasso Distribution: Properties, Sampling Methods, and Applications in Bayesian Lasso Regression

摘要： 在本文中，我们引入了一种新的概率分布，即Lasso分布。我们推导了该分布的几个基本性质，包括其矩和矩生成函数的显式表达式。此外，我们提出了一种高效且数值稳定的算法，用于从该分布生成随机样本，从而便于其在理论和应用设置中的使用。我们证明了Lasso分布属于指数族。Lasso分布的一个直接应用出现在现有的Gibbs采样器背景下，其中每个回归系数的完整条件分布遵循该分布。这导致了一个计算更高效且理论基础更牢固的采样方案。为了促进我们方法的应用，我们提供了一个R包BayesianLasso，可在CRAN上获得，实现了所提出的方法。我们的研究结果为Lasso惩罚背后的概率结构提供了新的见解，并在高维回归问题的贝叶斯推断中提供了实际改进。 显示英文摘要

摘要： In this paper, we introduce a new probability distribution, the Lasso distribution. We derive several fundamental properties of the distribution, including closed-form expressions for its moments and moment-generating function. Additionally, we present an efficient and numerically stable algorithm for generating random samples from the distribution, facilitating its use in both theoretical and applied settings. We establish that the Lasso distribution belongs to the exponential family. A direct application of the Lasso distribution arises in the context of an existing Gibbs sampler, where the full conditional distribution of each regression coefficient follows this distribution. This leads to a more computationally efficient and theoretically grounded sampling scheme. To facilitate the adoption of our methodology, we provide an R package, BayesianLasso, available on CRAN, implementing the proposed methods. Our findings offer new insights into the probabilistic structure underlying the Lasso penalty and provide practical improvements in Bayesian inference for high-dimensional regression problems.