Is the USDB interaction unique?

The USDB interaction is a gold standard of phenomenological shell model interactions. Its 66 coupling coefficients, or matrix elements, were fit to 608 experimental data points across 77 nuclei in the sd-shell. The uncertainty of USDB is typically cited as around 150 keV per energy level; this figure being the average error relative to the training data evaluated at the optimum parameter values. Principle component analysis assuming normality of the errors supports that this is a fair assessment and reconfirmed that only a small number of linear combinations of the 66 coupling coefficients are substantially constrained by the data. We have taken the next step with Bayesian uncertainty quantification: we refit the famous sd-shell interaction using Markov Chain Monte Carlo, together with an eigenvector continuation emulator of an exact shell model.