Bayesian Analysis with Markov Chain Monte Carlo for Global Optimization and Degeneracy Diagnosis in Nuclear Mass Models

We employ a full Bayesian analysis with adaptive Metropolis-Hastings Markov chain Monte Carlo (BA-MCMC) sampling to systematically study the posterior probability distributions of the strengths of energy terms in optimized nuclear mass models of Bethe-Weizs\"{a}cker variants. Strong correlations of some energy terms for some mass models are revealed through the parameter degeneracy diagnosis. We analyze selected refined models to determine parameter degeneracies while proposing a new macroscopic-microscopic mass model, BWL, which considers quadrupole and high-multipole deformation and shell corrections. All mass models in this work are analyzed and optimized through the BA-MCMC method. Compared with 2242 precise experimental binding energies of AME2020, BWL produces a root-mean-square deviation of 759 keV, particularly improving the description of masses in the light-nuclei and actinide regions. BA-MCMC offers robust inference on parameter degeneracy while providing an optimization method for future nuclear mass models.