Computing with Confidence: Imprecise Posteriors and Predictive Distributions

• DOI: 10.1061/9780784413609.091
• Publication Date: 2014-07-07T18:43:11Z
• Authors: Scott Ferson; Jason O'Rawe; Michael Balch
• Keywords: Confidence distribution; Coverage probability; Confidence region; Credible interval; Robust confidence intervals

Confidence structures (c-boxes) are imprecise generalizations of confidence distributions. They encode frequentist intervals at every level for parameters interest and, thereby, characterize the inferential uncertainty about distribution estimated from sparse or sample data. have a purely interpretation that makes them useful in engineering because they offer guarantee statistical performance through repeated use. Unlike traditional intervals, which cannot usually be propagated mathematical calculations, c-boxes can used calculations using standard methods probability bounds analysis and yield results also admit same interpretation. This means analysts now literally compute with confidence. We provide formulas several important problems, including parametric nonparametric estimation random The characterizations analogous to posterior distributions predictive contrast this c-box approach maximum likelihood Bayesian methods.