Marginal Inferential Models: Prior-Free Probabilistic Inference on Interest Parameters

• 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 AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2014.985827
• 发表日期: 2015
• 页码: 1621-1631
• 关键词: generalized fiducial-inference; behrens-fisher problem; statistical-inference; gamma-distribution; weak beliefs; confidence; FRAMEWORK; posterior; ARGUMENT

摘要

The inferential models (IM) framework provides prior-free, frequency-calibrated, and posterior probabilistic inference. The key is the use of random sets to predict unobservable auxiliary variables connected to the observable data and unknown parameters. When nuisance parameters are present, a marginalization step can reduce the dimension of the auxiliary variable which, in turn, leads to more efficient inference. For regular problems, exact marginalization can be achieved, and we give conditions for marginal IM validity. We show that our approach provides exact and efficient marginal inference in several challenging problems, including a many-normal-means problem. In nonregular problems, we propose a generalized marginalization technique and prove its validity. Details are given for two benchmark examples, namely, the Behrens-Fisher and gamma mean problems.