2014/12/16 by Ryan Martin, Martin, Ryan, Huiping Xu +5
Computer Science · Mathematics · #Advanced Statistical Methods and Models #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #stat.ME #stat.TH
paper · pdf · doi:10.48550/arxiv.1412.5139
24 pages, 4 figures, 2 pages of supplementary material
openalex publication_date 2014/12/16 · arxiv created 2016/06/06 · arxiv updated 2016/06/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In scientific applications, there often are several competing models that could be fit to the observed data, so quantification of the model uncertainty is of fundamental importance. In this paper, we develop an inferential model (IM) approach for simultaneously valid probabilistic inference over a collection of assertions of interest without requiring any prior input. Our construction guarantees that the approach is optimal in the sense that it is the most efficient among those which are valid. Connections between the IM's simultaneous validity and post-selection inference are also made. We apply the general results to obtain valid uncertainty quantification about the set of predictor variables to be included in a linear regression model.