On Bayesian oracle properties

Wenxin Jiang, Cheng Li*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

When model uncertainty is handled by Bayesian model averaging (BMA) or Bayesian model selection (BMS), the posterior distribution possesses a desirable "oracle property" for parametric inference, if for large enough data it is nearly as good as the oracle posterior, obtained by assuming unrealistically that the true model is known and only the true model is used. We study the oracle properties in a very general context of quasi-posterior, which can accommodate non-regular models with cubic root asymptotics and partial identification. Our approach for proving the oracle properties is based on a unified treatment that bounds the posterior probability of model mis-selection. This theoretical framework can be of interest to Bayesian statisticians who would like to theoretically justify their new model selection or model averaging methods in addition to empirical results. Furthermore, for non-regular models, we obtain nontrivial conclusions on the choice of prior penalty on model complexity, the temperature parameter of the quasi-posterior, and the advantage of BMA over BMS.

Original languageEnglish (US)
Pages (from-to)235-260
Number of pages26
JournalBayesian Analysis
Volume14
Issue number1
DOIs
StatePublished - Jan 1 2019

Keywords

  • Bayesian model selection
  • Consistency
  • Cubic root asymptotics
  • Model averaging
  • Oracle property
  • Partial identification

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics

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