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On Bayesian Oracle Properties
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.Comment: 31 page
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