Nonasymptotic Bounds for Bayesian Order Identification with Application to Mixtures

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 bounds. The results applyto mixture models. In this case, the underestimation probabilitiesare bounded by a constant times e-an (some a > 0, all sample sizen 1). The overestimation probabilities are bounded by 1/pn (alln larger than a known integer), up to a log n factor.