Moving Beyond Chi-Squared in Nuclei and Neutron Stars

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.