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In this paper, we construct a Bayesian posterior distribution using an appropriate data-dependent prior and develop its asymptotic concentration properties using new theoretical techniques. In particular, we leverage Spokoiny\u2019s powerful nonasymptotic theory to obtain sharp quadratic approximations of the GLM\u2019s log-likelihood function, which leads to tight bounds on the errors associated with the model-specific maximum likelihood estimators and the Laplace approximation of our Bayesian marginal likelihood. In turn, these improved bounds lead to significantly stronger, near-optimal Bayesian model selection consistency results, for example, far weaker beta-min conditions, compared to those available in the existing literature. In particular, our results are applicable to the Poisson regression model, in which the score function is not sub-Gaussian.<\/jats:p>","DOI":"10.1214\/25-aos2528","type":"journal-article","created":{"date-parts":[[2025,11,10]],"date-time":"2025-11-10T07:59:14Z","timestamp":1762761554000},"page":"2012-2039","source":"Crossref","is-referenced-by-count":2,"title":["Advances in Bayesian model selection consistency for high-dimensional generalized linear models"],"prefix":"10.1214","volume":"53","author":[{"given":"Jeyong","family":"Lee","sequence":"first","affiliation":[{"name":"Department of Industrial and Management Engineering, Pohang University of Science and Technology"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6495-9558","authenticated-orcid":false,"given":"Minwoo","family":"Chae","sequence":"additional","affiliation":[{"name":"Department of Industrial and Management Engineering, Pohang University of Science and Technology"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0760-9145","authenticated-orcid":false,"given":"Ryan","family":"Martin","sequence":"additional","affiliation":[{"name":"Department of Statistics, North Carolina State University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"108","reference":[{"key":"67","doi-asserted-by":"crossref","unstructured":"Yang, Y.<\/small>, Wainwright, M. 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