  We derive some simple relations that demonstrate how the posterior
convergence rate is related to two driving factors: a "penalized divergence" of
the prior, which measures the ability of the prior distribution to propose a
nonnegligible set of working models to approximate the true model and a "norm
complexity" of the prior, which measures the complexity of the prior support,
weighted by the prior probability masses. These formulas are explicit and
involve no essential assumptions and are easy to apply. We apply this approach
to the case with model averaging and derive some useful oracle inequalities
that can optimize the performance adaptively without knowing the true model.
