title: Mathematical Foundations for a Theory of Confidence Structures.
abstract: This paper introduces a new mathematical object: the confidence structure. A confidence structure represents inferential uncertainty in an unknown parameter by defining a belief function whose output is commensurate with Neyman-Pearson confidence. Confidence structures on a group of input variables can be propagated through a function to obtain a valid confidence structure on the output of that function. The theory of confidence structures is created by enhancing the extant theory of confidence distributions with the mathematical generality of Dempster-Shafer evidence theory. Mathematical proofs grounded in random set theory demonstrate the operative properties of confidence structures. The result is a new theory which achieves the holistic goals of Bayesian inference while maintaining the empirical rigor of frequentist inference.
authors.affiliation: Applied Biomathematics, 100 N Country Rd, Setauket, NY 11733, USA.
authors.forename: Michael Scott
authors.initials: MS
authors.lastname: Balch
keywords: Cartesian product; Dempster-Shafer; confidence distribution; p-value; random set