There has been significant progress in Bayesian inference based on sparsity-inducing (e.g., spike-and-slab and horseshoe-type) priors for high-dimensional regression models. The resulting posteriors, however, in general do not possess desirable frequentist properties, and the credible sets thus cannot serve as valid confidence sets even asymptotically. We introduce a novel debiasing approach that corrects the bias for the entire Bayesian posterior distribution. We establish a new Bernstein-von Mises theorem that guarantees the frequentist validity of the debiased posterior. We demonstrate the practical performance of our proposal through Monte Carlo simulations and two empirical applications in economics.

翻译：基于稀疏诱导先验（如钉板先验和马蹄型先验）的高维回归模型贝叶斯推断已取得显著进展。然而，所得后验分布通常不具备理想的频率性质，其可信区间即使在渐近意义上也无法作为有效的置信集。本文提出一种新颖的去偏方法，用于校正整个贝叶斯后验分布的偏差。我们建立了一个新的伯恩斯坦-冯·米塞斯定理，确保去偏后验的频率有效性。通过蒙特卡洛模拟和经济学中的两个实证应用，我们验证了所提方法的实际性能。