Ryan Martin of Purdue University : Imprecision is imperative for reliable uncertainty quantification

Posted by Min Yang , part of the Departmental Colloquium.

At

Sept. 25, 2026, 3 p.m.

In

636 SEO

Abstract

Whether it's statistics, machine learning, or artificial intelligence, a quantification of uncertainty is key to making decisions and, therefore, reliability is essential. The oldest approach to uncertainty quantification is Bayesian: define (precise) prior probabilities for the relevant unknowns, and use observations to update these to (precise) posterior probabilities. Naturally, the reliability of the posterior probabilities is closely related to the suitability of the prior probabilities. In most applications, however, a priori beliefs are largely vacuous and, since no precise probability can represent ignorance, there is reason to question the reliability of the posterior probabilities. The false confidence theorem says that, in a sense to be described formally, no data-driven precise probability (Bayesian or otherwise) quantifies uncertainty reliably. If no precise probability can do the job reliably, then we must need an imprecise probability -- hence, imprecision is imperative. To keep the "IM" wordplay going, I'll argue that the imperative imprecision isn't impossible to efficiently implement, using what I call a possibilistic inferential model (IM). Moreover, those methods that are reliable in the more familiar frequentist sense, such as conformal prediction, can easily be transformed into a possibilistic IM whose uncertainty quantification achieves the desired reliability properties.