Bounds for Bayesian order identification with application to mixtures

Abstract

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.

Published in at http://dx.doi.org/10.1214/009053607000000857 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)