Title: On the Posterior Computation Under the Dirichlet-Laplace Prior Show Chinese title

Title: 在狄利克雷-拉普拉斯先验下的后验计算

Abstract: Modern applications routinely collect high-dimensional data, leading to statistical models having more parameters than there are samples available. A common solution is to impose sparsity in parameter estimation, often using penalized optimization methods. Bayesian approaches provide a probabilistic framework to formally quantify uncertainty through shrinkage priors. Among these, the Dirichlet-Laplace prior has attained recognition for its theoretical guarantees and wide applicability. This article identifies a critical yet overlooked issue in the implementation of Gibbs sampling algorithms for such priors. We demonstrate that ambiguities in the presentation of key algorithmic steps, while mathematically coherent, have led to widespread implementation inaccuracies that fail to target the intended posterior distribution -- a target endowed with rigorous asymptotic guarantees. Using the normal-means problem and high-dimensional linear regressions as canonical examples, we clarify these implementation pitfalls and their practical consequences and propose corrected and more efficient sampling procedures. Show Chinese abstract

Abstract: 现代应用通常会收集高维数据，导致统计模型中的参数数量多于可用样本数量。 一种常见的解决方案是通过惩罚优化方法在参数估计中引入稀疏性。 贝叶斯方法提供了一个概率框架，通过收缩先验来正式量化不确定性。 其中，狄利克雷-拉普拉斯先验因其理论保证和广泛适用性而受到认可。 本文指出了在这些先验的吉布斯抽样算法实现中一个关键但被忽视的问题。 我们证明了关键算法步骤表述中的歧义，在数学上是自洽的，但导致了广泛存在的实现错误，这些错误未能针对预期的后验分布——该分布具有严格的渐近保证。 通过正态均值问题和高维线性回归作为典型例子，我们澄清了这些实现缺陷及其实际后果，并提出了修正且更高效的抽样过程。