STATISTICS Seminars Series: Max Raner

Topic False Confidence, Beyond Additivity, and Possib(ilistical)ly a Fusion of the Frequentist and Bayesian

Abstract The quest for the “holy grail” of statistical theory: a posterior distribution without the need for subjective priors, has generated many proposals over the last century. The recent False Confidence Theorem has shown that additive probability measures inevitably risk false certainty, casting doubt not only on these proposed methods, but on probability itself as the language for epistemic uncertainty. A natural way forward is to move beyond additivity, into the framework of imprecise probability. Among these, possibility theory stands out: it is simple, elegant, and uniquely well aligned with the needs of statistical inference, with direct connections to p-values, confidence sets, and hypothesis tests. Possibility offers a language more primitive than probability, and perhaps a bridge between Bayesian and frequentist paradigms—with new territory inbetween. In this talk, I will trace the historical context of this problem, introduce possibility theory and its relation to classical theory, and discuss recent developments and open directions for research.