Moving Beyond Chi-Squared in Nuclei and Neutron Stars

TL;DR

This paper discusses how Bayesian inference can improve data analysis in nuclear physics and neutron star research by moving beyond traditional Gaussian likelihood assumptions, leading to less biased and more accurate predictions.

Contribution

It introduces a Bayesian approach to replace Gaussian likelihood assumptions in nuclear physics analyses, demonstrating its advantages through neutron star and nuclear mass data applications.

Findings

Gaussian likelihood approximation can bias nuclear mass predictions.

Bayesian inference provides more accurate constraints on nuclear symmetry energy.

Improved analysis methods enhance understanding of dense matter and nuclear properties.

Abstract

There are several assumptions made in a standard $\chi^2$ analysis of data, including the frequent assumption that the likelihood function is well approximated by a multivariate Gaussian distribution. This article briefly reviews the standard approach and describes how Bayesian inference can be used to go beyond the assumption that the likelihood is Gaussian. Two separate types of analysis relevant to nuclear physics are used as test cases. The first is the determination of the equation of state of dense matter from neutron star mass and radius data. The second is the use of theoretical nuclear mass models to fit currently available data and predict the value of masses which have not yet been measured. For the problem of predicting nuclear masses, it is demonstrated that approximating the likelihood function with a Gaussian can produce biased predictions of unmeasured masses. Finally, the lessons learned from these fitting problems are used to propose a method for improving constraints on the nuclear symmetry energy.