Bounds for Bayesian order identification with application to mixtures

TL;DR

This paper establishes new bounds for Bayesian order estimators using nonparametric techniques, demonstrating exponential and polynomial decay rates of errors in mixture models, which enhances understanding of model complexity estimation.

Contribution

It introduces novel underestimation and overestimation bounds for Bayesian order estimators applicable to mixture models, with explicit error rate characterizations.

Findings

Errors decay exponentially in mixture models

Errors decay at a rate of $(rac{ ext{log } n)^b}{ ext{sqrt } n}$

Bounds are derived using nonparametric techniques

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.