This paper uses a full Bayesian analysis with adaptive Metropolis–Hastings Markov chain Monte Carlo (BA-MCMC) sampling to study and optimize models for nuclear binding energies. The authors apply the method to variants of the Bethe–Weizsäcker semi‑empirical mass formula, map the full posterior probability distributions of the model parameters, diagnose strong correlations (parameter degeneracies), and propose a new macroscopic‑microscopic mass model called BWL. When compared with 2242 precise experimental binding energies from AME2020, BWL gives a root‑mean‑square deviation of 759 keV, with particular improvement for light nuclei and actinides.

The Bethe–Weizsäcker family of models treats a nucleus roughly like a liquid drop and represents the binding energy as a sum of physical terms such as volume, surface, Coulomb (electrostatic) and symmetry energies. Many refinements over the decades have added terms such as Coulomb exchange, pairing, surface symmetry, curvature and shell corrections. But most previous variants still neglected deformation effects systematically and showed systematic discrepancies in strongly deformed regions, for example in rare‑earth and actinide nuclei.

To address both parameter uncertainty and missing deformation effects, the authors run BA‑MCMC to sample the joint posterior distributions of the energy‑term strengths in several BW (Bethe‑Weizsäcker) variants. Markov chain Monte Carlo sampling produces many parameter samples from the posterior distribution; inspecting these samples reveals how parameters covary and whether different combinations of parameters give similar fits (degeneracy). The paper also uses the Spearman rank correlation (a rank‑based measure) to detect nonlinear correlations that linear measures like Pearson’s coefficient can miss. Using these tools the authors identify strong correlations in some models and construct the BWL model that explicitly includes quadrupole and higher‑multipole deformation terms together with shell corrections.