Quantifying statistical uncertainties in ab initio nuclear physics using Lagrange multipliers

TL;DR

This paper compares methods for quantifying statistical uncertainties in ab initio nuclear physics, highlighting the robustness of Lagrange multipliers over covariance-based approaches.

Contribution

It introduces and evaluates the Lagrange multipliers method for uncertainty quantification, demonstrating its advantages over traditional covariance-based methods in nuclear physics.

Findings

Lagrange multipliers method is more robust.

Covariance-based methods are less demanding computationally.

Uncertainty propagation affects predictions for light-mass nuclei.

Abstract

Theoretical predictions need quantified uncertainties for a meaningful comparison to experimental results. This is an idea which presently permeates the field of theoretical nuclear physics. In light of the recent progress in estimating theoretical uncertainties in ab initio nuclear physics, we here present and compare methods for evaluating the statistical part of the uncertainties. A special focus is put on the (for the field) novel method of Lagrange multipliers (LM). Uncertainties from the fit of the nuclear interaction to experimental data are propagated to a few observables in light-mass nuclei to highlight any differences between the presented methods. The main conclusion is that the LM method is more robust, while covariance based methods are less demanding in their evaluation.