# Debiased Bayesian Inference for High-dimensional Regression Models

arXiv: https://arxiv.org/abs/2512.09257 · HTML: https://mlsanity.com/paper/2512.09257/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- First posted on arXiv 10 Dec 2025.

## Abstract (arXiv)

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.