Table of Contents
International Scholarly Research Notices
Volume 2014, Article ID 469340, 8 pages
http://dx.doi.org/10.1155/2014/469340
Research Article

Some Simple Formulas for Posterior Convergence Rates

Department of Statistics, Northwestern University, Evanston, IL 60208, USA

Received 25 June 2014; Accepted 15 August 2014; Published 29 October 2014

Academic Editor: Yuehua Wu

Copyright © 2014 Wenxin Jiang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We derive some simple relations that demonstrate how the posterior convergence rate is related to two driving factors: a “penalized divergence” of the prior, which measures the ability of the prior distribution to propose a nonnegligible set of working models to approximate the true model and a “norm complexity” of the prior, which measures the complexity of the prior support, weighted by the prior probability masses. These formulas are explicit and involve no essential assumptions and are easy to apply. We apply this approach to the case with model averaging and derive some useful oracle inequalities that can optimize the performance adaptively without knowing the true model.