We derive some simple relations that demonstrate how the posterior convergence rate is related to two driving factors: a ââ?¬Å?penalized\ndivergenceââ?¬Â of the prior, which measures the ability of the prior distribution to propose a non negligible set of working models to\napproximate the true model and a ââ?¬Å?norm complexityââ?¬Â of the prior, which measures the complexity of the prior support, weighted by\nthe prior probability masses. These formulas are explicit and involve no essential assumptions and are easy to apply.We apply this\napproach to the case with model averaging and derive some useful oracle inequalities that can optimize the performance adaptively\nwithout knowing the true model.
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