In numerous Bayesian procedures, especially for high-dimensional models, certain prior choices induce posterior distributions with optimal properties, according to some frequentist criteria. This note offers a unified treatment of such priors through the notion of oracle priors. Several examples from the most recent literature are considered, illustrating the impact of these priors on statistical inference in specific cases.

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Oracle Priors in Bayesian Inference: a Frequentist View

  • Stefano Rizzelli

摘要

In numerous Bayesian procedures, especially for high-dimensional models, certain prior choices induce posterior distributions with optimal properties, according to some frequentist criteria. This note offers a unified treatment of such priors through the notion of oracle priors. Several examples from the most recent literature are considered, illustrating the impact of these priors on statistical inference in specific cases.