The efficiency of two Bayesian order estimators is studied underweak assumptions. By using nonparametric techniques, we prove newnonasymptotic underestimation and overestimation bounds. The boundscompare favorably with optimal bounds yielded by the Stein lemmaand also with other known asymptotic...

We derive rates of contraction of posterior distributions on nonparametric models resulting from sieve priors. The aim of the paper is to provide general conditions to get posterior rates when the parameter space has a general structure, and rate adaptation when the parameter space is, e.g., a...