Frequentist model comparison based on covariance analysis: The case of the nuclear liquid-drop model

Quantifying intermodel uncertainties has gained increasing attention in nuclear theory. In this work, we extend the least-squares covariance analysis method-----commonly used to quantify parameter uncertainties in nuclear energy density functionals (EDFs)-----to address intermodel uncertainty. Two criteria are proposed, motivated by the Laplace approximation to the Bayesian posterior, for frequentist model selection and averaging. As a case study, we compare two liquid-drop models that differ in the form of the symmetry energy term, using both covariance analysis and Bayesian inference. The proposed criteria incorporate parameter uncertainties and correlations, and are shown to serve as efficient surrogates for Bayesian evidence and its variant. Given their computational efficiency, the two criteria are promising tools for addressing model dependence issues in studies based on deterministic theoretical models. In particular, frequentist model comparison based on the two criteria provides a feasible means to quantify intermodel uncertainties among the many widely used nuclear EDFs that have been supplemented with covariance analysis following calibration.