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A Note on Bayesian Oracle Properties

21 July 2015
Wenxin Jiang
Cheng Li
ArXiv (abs)PDFHTML
Abstract

We establish a fundamental relation between three different topics: Bayesian model selection, model averaging, and oracle performance. The relatively basic property of model selection consistency is shown to be equivalent to a seemingly more advanced distributional result, the oracle property. The result is very simple and general. There is no restriction on the type of prior or likelihood function used, or on the limiting distribution of the oracle posterior. A number of possible applications are discussed.

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