Foundations of Statistics

A Bayesian Decision-Theoretic Approach to Logically-Consistent Hypothesis Testing

This work addresses an important issue regarding the performance of simultaneous test procedures: the construction of multiple tests that at the same time are optimal from a statistical perspective and that also yield logically-consistent results …

The Logical Consistency of Simultaneous Agnostic Hypothesis Tests

Simultaneous hypothesis tests can fail to provide results that meet logical requirements. For example, if A and B are two statements such that A implies B, there exist tests that, based on the same data, reject B but not A. Such outcomes are …