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Title: On Bayesian oracle properties
Authors: Jiang, W.
Li, C. 
Keywords: Bayesian model selection
Cubic root asymptotics
Model averaging
Oracle property
Partial identification
Issue Date: 2019
Publisher: International Society for Bayesian Analysis
Citation: Jiang, W., Li, C. (2019). On Bayesian oracle properties. Bayesian Analysis 14 (1) : 235-260. ScholarBank@NUS Repository.
Rights: Attribution 4.0 International
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. © 2019 International Society for Bayesian Analysis.
Source Title: Bayesian Analysis
ISSN: 1936-0975
DOI: 10.1214/18-BA1097
Rights: Attribution 4.0 International
Appears in Collections:Staff Publications

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