  The efficiency of two Bayesian order estimators is studied. By using
nonparametric techniques, we prove new underestimation and overestimation
bounds. The results apply to various models, including mixture models. In this
case, the errors are shown to be $O(e^{-an})$ and $O((\log n)^b/\sqrt{n})$
($a,b>0$), respectively.
