THE BERNSTEIN-VON MISES THEOREM AND NONREGULAR MODELS

• 成果类型: Article
• 署名作者: Bochkina, Natalia A.; Green, Peter J.
• 署名单位: University of Edinburgh; University of Bristol; University of Technology Sydney
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/14-AOS1239
• 发表日期: 2014
• 页码: 1850-1878
• 关键词: likelihood ratio tests; bayesian reconstructions; emission-tomography; distributions; Consistency

摘要

We study the asymptotic behaviour of the posterior distribution in a broad class of statistical models where the true solution occurs on the boundary of the parameter space. We show that in this case Bayesian inference is consistent, and that the posterior distribution has not only Gaussian components as in the case of regular models (the Bernstein-von Mises theorem) but also has Gamma distribution components whose form depends on the behaviour of the prior distribution near the boundary and have a faster rate of convergence. We also demonstrate a remarkable property of Bayesian inference, that for some models, there appears to be no bound on efficiency of estimating the unknown parameter if it is on the boundary of the parameter space. We illustrate the results on a problem from emission tomography.