Posterior contraction in sparse generalized linear models

Seonghyun Jeong, Subhashis Ghosal

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


We study posterior contraction rates in sparse high-dimensional generalized linear models using priors incorporating sparsity. A mixture of a point mass at zero and a continuous distribution is used as the prior distribution on regression coefficients. In addition to the usual posterior, the fractional posterior, which is obtained by applying Bayes theorem with a fractional power of the likelihood, is also considered. The latter allows uniformity in posterior contraction over a larger subset of the parameter space. In our set-up, the link function of the generalized linear model need not be canonical. We show that Bayesian methods achieve convergence properties analogous to lasso-type procedures. Our results can be used to derive posterior contraction rates in many generalized linear models including logistic, Poisson regression and others.

Original languageEnglish
Pages (from-to)367-379
Number of pages13
Issue number2
Publication statusPublished - 2021 Jun 1

Bibliographical note

Publisher Copyright:
© 2020 Biometrika Trust.

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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