Debiased Bayesian Inference for High-dimensional Regression Models
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908703552176128 |
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| author | Chen, Qihui Fang, Zheng Liu, Ruixuan |
| author_facet | Chen, Qihui Fang, Zheng Liu, Ruixuan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_09257 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Debiased Bayesian Inference for High-dimensional Regression Models Chen, Qihui Fang, Zheng Liu, Ruixuan Econometrics Statistics Theory Computation Methodology Machine Learning 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. |
| title | Debiased Bayesian Inference for High-dimensional Regression Models |
| topic | Econometrics Statistics Theory Computation Methodology Machine Learning |
| url | https://arxiv.org/abs/2512.09257 |