Gaussian approximation of general non-parametric posterior distributions

Zuofeng Shang, Guang Cheng

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


In a general class of Bayesian non-parametric models, we prove that the posterior distribution can be asymptotically approximated by a Gaussian process (GP). Our results apply to non-parametric exponential family that contains both Gaussian and non-Gaussian regression and also hold for both efficient (root-n) and inefficient (non-root-n) estimations. Our general approximation theorem does not rely on posterior conjugacy and can be verified in a class of GP priors that has a smoothing spline interpretation. In particular, the limiting posterior measure becomes prior free under a Bayesian version of 'under-smoothing' condition. Finally, we apply our approximation theorem to examine the asymptotic frequentist properties of Bayesian procedures such as credible regions and credible intervals.

Original languageEnglish (US)
Pages (from-to)509-529
Number of pages21
JournalInformation and Inference
Issue number3
StatePublished - Sep 19 2018
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Computational Theory and Mathematics
  • Analysis
  • Applied Mathematics
  • Statistics and Probability
  • Numerical Analysis


  • Bayesian inference
  • Frequentist validity
  • Gaussian approximation
  • Non-parametric exponential family
  • Smoothing spline


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