  In this paper, we consider the problem of quantifying parametric uncertainty
in classical empirical interatomic potentials (IPs) using both Bayesian (Markov
Chain Monte Carlo) and frequentist (profile likelihood) methods. We interface
these tools with the Open Knowledgebase of Interatomic Models and study three
models based on the Lennard-Jones, Morse, and Stillinger--Weber potentials. We
confirm that IPs are typically sloppy, i.e., insensitive to coordinated changes
in some parameter combinations. Because the inverse problem in such models is
ill-conditioned, parameters are unidentifiable. This presents challenges for
traditional statistical methods, as we demonstrate and interpret within both
Bayesian and frequentist frameworks. We use information geometry to illuminate
the underlying cause of this phenomenon and show that IPs have global
properties similar to those of sloppy models from fields such as systems
biology, power systems, and critical phenomena. IPs correspond to bounded
manifolds with a hierarchy of widths, leading to low effective dimensionality
in the model. We show how information geometry can motivate new, natural
parameterizations that improve the stability and interpretation of uncertainty
quantification analysis and further suggest simplified, less-sloppy models.
