  Until recently, uncertainty quantification in low energy nuclear theory was
typically performed using frequentist approaches. However in the last few
years, the field has shifted toward Bayesian statistics for evaluating
confidence intervals. Although there are statistical arguments to prefer the
Bayesian approach, no direct comparison is available. In this work, we compare,
directly and systematically, the frequentist and Bayesian approaches to
quantifying uncertainties in direct nuclear reactions. Starting from identical
initial assumptions, we determine confidence intervals associated with the
elastic and the transfer process for both methods, which are evaluated against
data via a comparison of the empirical coverage probabilities. Expectedly, the
frequentist approach is not as flexible as the Bayesian approach in exploring
parameter space and often ends up in a different minimum. We also show that the
two methods produce significantly different correlations. In the end, the
frequentist approach produces significantly narrower uncertainties on the
considered observables than the Bayesian. Our study demonstrates that the
uncertainties on the reaction observables considered here within the Bayesian
approach represent reality more accurately than the much narrower uncertainties
obtained using the standard frequentist approach.
