Bernstein-von Mises Theorem for Sparse Generalized Linear Model
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918524721561600 |
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| author | Li, Hanqing Lu, Xuewen |
| author_facet | Li, Hanqing Lu, Xuewen |
| contents | We study spike-and-slab priors for generalized linear models with possible grouped sparsity. The main result is an oracle Bernstein--von Mises theorem for the fractional posterior under supportwise likelihood assumptions. The proof develops sparse local asymptotic normality and Laplace approximation around support-specific pseudo-true centers, and combines them with fixed-prior mass, support penalization, recovery geometry, and beta-min separation to obtain contraction, support recovery, Gaussian mixture approximation, and collapse to the oracle Gaussian law. Model-entry verifications are given for Gaussian regression and for logistic, Poisson, probit, Gamma log-link, and negative-binomial log-link regression under stated sufficient conditions. The ordinary posterior is treated only through restricted Gaussian and canonical-link extensions, with coverage under additional active-dimension and moment conditions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_27137 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bernstein-von Mises Theorem for Sparse Generalized Linear Model Li, Hanqing Lu, Xuewen Statistics Theory Methodology 62G20, 62F15 (Primary) 62J12 (Secondary) We study spike-and-slab priors for generalized linear models with possible grouped sparsity. The main result is an oracle Bernstein--von Mises theorem for the fractional posterior under supportwise likelihood assumptions. The proof develops sparse local asymptotic normality and Laplace approximation around support-specific pseudo-true centers, and combines them with fixed-prior mass, support penalization, recovery geometry, and beta-min separation to obtain contraction, support recovery, Gaussian mixture approximation, and collapse to the oracle Gaussian law. Model-entry verifications are given for Gaussian regression and for logistic, Poisson, probit, Gamma log-link, and negative-binomial log-link regression under stated sufficient conditions. The ordinary posterior is treated only through restricted Gaussian and canonical-link extensions, with coverage under additional active-dimension and moment conditions. |
| title | Bernstein-von Mises Theorem for Sparse Generalized Linear Model |
| topic | Statistics Theory Methodology 62G20, 62F15 (Primary) 62J12 (Secondary) |
| url | https://arxiv.org/abs/2605.27137 |