  Uncertainty quantification has become increasingly more prominent in nuclear
physics over the past several years. In few-body reaction theory, there are
four main sources that contribute to the uncertainties in the calculated
observables: the effective potentials, approximations made to the few-body
problem, structure functions, and degrees of freedom left out of the model
space. In this work, we illustrate some of the features that can be obtained
when modern statistical tools are applied in the context of nuclear reactions.
This work consists of a summary of the progress that has been made in
quantifying theoretical uncertainties in this domain, focusing primarily on
those uncertainties coming from the effective optical potential as well as
their propagation within various reaction theories. We use, as the central
example, reactions on the doubly-magic stable nucleus $^{40}$Ca, namely neutron
and proton elastic scattering and single-nucleon transfer
$^{40}$Ca(d,p)$^{41}$Ca. First, we show different optimization schemes used to
constrain the optical potential from differential cross sections and other
experimental constraints; we then discuss how these uncertainties propagate to
the transfer cross section, comparing two reaction theories. We finish by
laying out our future plans.
