Bee Swarm Metropolis–Hastings Sampling for Bayesian Inference in the Ginzburg–Landau Equation

• Published in: Algorithms Vol. 18; no. 8; p. 476
• Main Authors: Xia, Shucan, Zhang, Lipu
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.08.2025
• Subjects: Adaptation; Adaptive sampling; Adjustment; Algorithms; Bayesian analysis; Bayesian parameter inference; bee swarm algorithm; Bees; Collaboration; Design; Efficiency; Exploitation; Ginzburg–Landau model; Information sharing; Landau-Ginzburg equations; Markov analysis; Markov chains; Markov processes; Methods; Metropolis–Hastings sampling; Monte Carlo method; Optimization; Parameter estimation; Sampling methods; Solitary waves; Statistical inference; Swarm intelligence
• ISSN: 1999-4893; 1999-4893
• DOI: 10.3390/a18080476

To improve the sampling efficiency of Markov Chain Monte Carlo in complex parameter spaces, this paper proposes an adaptive sampling method that integrates a swarm intelligence mechanism called the BeeSwarm-MH algorithm. The method combines global exploration by scout bees with local exploitation by worker bees. It employs multi-stage perturbation intensities and adaptive step-size tuning to enable efficient posterior sampling. Focusing on Bayesian inference for parameter estimation in the soliton solutions of the two-dimensional complex Ginzburg–Landau equation, we design a dedicated inference framework to systematically compare the performance of BeeSwarm-MH with the classical Metropolis–Hastings algorithm. Experimental results demonstrate that BeeSwarm-MH achieves comparable estimation accuracy while significantly reducing the required number of iterations and total computation time for convergence. Moreover, it exhibits superior global search capabilities and adaptive features, offering a practical approach for efficient Bayesian inference in complex physical models.