Conditional inferential models: combining information for prior-free probabilistic inference

• 成果类型: Article
• 署名作者: Martin, Ryan; Liu, Chuanhai
• 署名单位: University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; Purdue University System; Purdue University
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12070
• 发表日期: 2015
• 页码: 195-217
• 关键词: generalized fiducial-inference; variance-components; confidence; distributions; estimator; FRAMEWORK; ancillary; posterior; belief

摘要

The inferential model (IM) framework provides valid prior-free probabilistic inference by focusing on predicting unobserved auxiliary variables. But, efficient IM-based inference can be challenging when the auxiliary variable is of higher dimension than the parameter. Here we show that features of the auxiliary variable are often fully observed and, in such cases, a simultaneous dimension reduction and information aggregation can be achieved by conditioning. This proposed conditioning strategy leads to efficient IM inference and casts new light on Fisher's notions of sufficiency, conditioning and also Bayesian inference. A differential-equation-driven selection of a conditional association is developed, and validity of the conditional IM is proved under some conditions. For problems that do not admit a conditional IM of the standard form, we propose a more flexible class of conditional IMs based on localization. Examples of local conditional IMs in a bivariate normal model and a normal variance components model are also given.