Posterior model consistency in high-dimensional Bayesian variable selection with arbitrary priors

Min Hua and Gyuhyeong Goh

Statistics & Probability Letters, 2025, vol. 223, issue C

Abstract: In the context of Bayesian regression modeling, posterior model consistency provides frequentist validation for Bayesian variable selection. A question that has long been open is whether posterior model consistency holds under arbitrary priors when high-dimensional variable selection is performed. In this paper, we aim to give an answer by establishing sufficient conditions for priors under which the posterior model distribution converges to a degenerate distribution at the true model. Our framework considers high-dimensional regression settings where the number of potential predictors grows at a rate faster than the sample size. We demonstrate that a wide selection of priors satisfy the conditions that we establish in this paper.

Keywords: Approximate marginal likelihood; Consistent Bayesian model selection; High-dimensional linear regression; Posterior model probability (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spl.2025.110415

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