Direct Comparison between Bayesian and Frequentist Uncertainty Quantification for Nuclear Reactions.

Area of Science:

• Nuclear Physics
• Computational Physics
• Statistical Analysis

Background:

• Uncertainty quantification in low energy nuclear theory traditionally used frequentist methods.
• Recent shifts in the field favor Bayesian statistics for confidence interval evaluation.
• Direct comparisons between frequentist and Bayesian uncertainty quantification in nuclear reactions are lacking.

Purpose of the Study:

• To systematically compare frequentist and Bayesian approaches for quantifying uncertainties in direct nuclear reactions.
• To evaluate confidence intervals for elastic and transfer processes using both methods.
• To assess the accuracy of each method against empirical data.

Main Methods:

• Direct, systematic comparison of frequentist and Bayesian uncertainty quantification.
• Determination of confidence intervals for elastic and transfer nuclear reactions.
• Evaluation of methods via empirical coverage probabilities against experimental data.

Main Results:

• Frequentist approach shows less flexibility in parameter space exploration, often converging to different minima.
• Significant differences observed in parameter correlations between the two methods.
• Frequentist approach yields narrower uncertainties on observables compared to the Bayesian approach.

Conclusions:

• The Bayesian approach provides a more accurate representation of uncertainties in direct nuclear reactions.
• Frequentist methods, while producing narrower uncertainties, may not accurately reflect the true uncertainty range.
• This study highlights the importance of choosing appropriate statistical methods for reliable uncertainty quantification in nuclear theory.