ASYMPTOTIC NORMALITY AND VALID INFERENCE FOR GAUSSIAN VARIATIONAL APPROXIMATION

• 成果类型: Article
• 署名作者: Hall, Peter; Tung Pham; Wand, M. P.; Wang, S. S. J.
• 署名单位: University of Melbourne; University of Wollongong; University of Technology Sydney
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/11-AOS908
• 发表日期: 2011
• 页码: 2502-2532
• 关键词: bayes

摘要

We derive the precise asymptotic distributional behavior of Gaussian variational approximate estimators of the parameters in a single-predictor Poisson mixed model. These results are the deepest yet obtained concerning the statistical properties of a variational approximation method. Moreover, they give rise to asymptotically valid statistical inference. A simulation study demonstrates that Gaussian variational approximate confidence intervals possess good to excellent coverage properties, and have a similar precision to their exact likelihood counterparts.