# Direct comparison between Bayesian and frequentist uncertainty quantification for nuclear reactions

## TL;DR

This paper systematically compares Bayesian and frequentist methods for uncertainty quantification in nuclear reactions, revealing that Bayesian approaches provide more accurate and flexible uncertainty estimates than traditional frequentist methods.

## Contribution

It provides the first direct comparison between Bayesian and frequentist uncertainty quantification methods in nuclear reaction analysis, highlighting their differences and advantages.

## Key findings

- Bayesian approach offers more flexible parameter exploration.
- Frequentist uncertainties are narrower than Bayesian ones.
- Bayesian uncertainties align better with empirical data.

## Abstract

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.