  Statistical tools of uncertainty quantification can be used to assess the
information content of measured observables with respect to present-day
theoretical models; to estimate model errors and thereby improve predictive
capability; to extrapolate beyond the regions reached by experiment; and to
provide meaningful input to applications and planned measurements. To showcase
new opportunities offered by such tools, we make a rigorous analysis of
theoretical statistical uncertainties in nuclear density functional theory
using Bayesian inference methods. By considering the recent mass measurements
from the Canadian Penning Trap at Argonne National Laboratory, we demonstrate
how the Bayesian analysis and a direct least-squares optimization, combined
with high-performance computing, can be used to assess the information content
of the new data with respect to a model based on the Skyrme energy density
functional approach. Employing the posterior probability distribution computed
with a Gaussian process emulator, we apply the Bayesian framework to propagate
theoretical statistical uncertainties in predictions of nuclear masses,
two-neutron dripline, and fission barriers. Overall, we find that the new mass
measurements do not impose a constraint that is strong enough to lead to
significant changes in the model parameters. The example discussed in this
study sets the stage for quantifying and maximizing the impact of new
measurements with respect to current modeling and guiding future experimental
efforts, thus enhancing the experiment-theory cycle in the scientific method.
