2013/06/30 by Ryan Martin, Chuanhai Liu · 66 citations
Computer Science · Mathematics · #Artificial intelligence #Bayesian Modeling and Causal Inference #Benchmark (surveying) #Computer science #Dimension (graph theory) #Econometrics #Inference #Marginal distribution #Mathematics #Nuisance parameter #Observable #Probabilistic logic #Random variable #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics #Unobservable #Variable elimination #math.ST #stat.ME #stat.TH
paper · pdf · doi:10.1080/01621459.2014.985827
published in Journal of the American Statistical Association 110(512), 1621-1631 · 23 pages, 2 figures
arxiv created 2014/10/24 · openalex publication_date 2014/11/15 · arxiv updated 2016/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.