标题：On Bayesian Oracle Properties
作者：Jiang, Wenxin; Li, Cheng
作者机构：[Jiang, Wenxin] Shandong Univ, Jinan, Shandong, Peoples R China.; [Jiang, Wenxin] Northwestern Univ, Evanston, IL 60208 USA.; [Li, Cheng] Natl Uni 更多
通讯作者地址：[Li, C]Natl Univ Singapore, Singapore, Singapore.
关键词：Bayesian model selection; consistency; model averaging; oracle property;; cubic root asymptotics; partial identification
摘要：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.