Valid Prior-Free Probabilistic Inference and Its Applications in Medical Statistics

Abstract

Abstract:Valid, prior-free, and situation-specific probabilistic inference is desirable for serious uncertain inference, especially in bio-medical statistics. This chapter * introduces such an inferential system, called the Inferential Model (IM) framework, proposed recently. IMs do not require a prior to be specified, yet they produce probabilistic inferential results that have desireable frequency properties. This chapter illustrates the IM framework and demonstrates its potential applications in bio-medical statistics with a collection of benchmark examples, including (i) classification, (ii) inference with subgroup selection, (iii) 2×2 tables, and (v) a many-normal-means problem in meta-analysis.