BeeSwarm-MH Sampling for Bayesian Inference of GL Equation Parameters

This study presents BeeSwarm-MH, a hybrid sampling algorithm integrating bee swarm optimization with Metropolis-Hastings (MH) criteria to address traditional MH's limitations in global exploration and step-size sensitivity. The algorithm achieves synergistic global-local search via scout-worker bee division, dual-layer adaptive step-size adjustment, and sliding-window convergence diagnosis.Experimental validation on Ginzburg-Landau equation parameter estimation shows BeeSwarm-MH reduces runtime by 65.3\% with 10\% fewer iterations compared to classic MH, yielding parameter deviations less than 0.001 and R-hat less than 1.0014. This work demonstrates that swarm intelligence-MCMC integration enhances inference efficiency for complex models, offering a novel paradigm for high-dimensional Bayesian analysis.Future research will explore high-dimensional extension, multi-modal convergence theory, and applications in quantum physics and biomedical modeling.