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

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  • Hua, Min
  • Goh, Gyuhyeong

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.

Suggested Citation

  • Hua, Min & Goh, Gyuhyeong, 2025. "Posterior model consistency in high-dimensional Bayesian variable selection with arbitrary priors," Statistics & Probability Letters, Elsevier, vol. 223(C).
    • Handle: RePEc:eee:stapro:v:223:y:2025:i:c:s0167715225000604
    DOI: 10.1016/j.spl.2025.110415
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    References listed on IDEAS

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    1. Chris Hans, 2009. "Bayesian lasso regression," Biometrika, Biometrika Trust, vol. 96(4), pages 835-845.
    2. A. Armagan & D. B. Dunson & J. Lee & W. U. Bajwa & N. Strawn, 2013. "Posterior consistency in linear models under shrinkage priors," Biometrika, Biometrika Trust, vol. 100(4), pages 1011-1018.
    3. Valen E. Johnson & David Rossell, 2012. "Bayesian Model Selection in High-Dimensional Settings," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 649-660, June.
    4. Wang, Hansheng, 2009. "Forward Regression for Ultra-High Dimensional Variable Screening," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1512-1524.
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