方法对比

	分层近似贝叶斯计算	分层马尔可夫链蒙特卡洛
领域	贝叶斯	贝叶斯
方法族	Bayesian methods	Bayesian methods
起源年份	2009–2010	1990
提出者	Toni, Welch, Strelkowa, Ipsen & Stumpf (building on Pritchard et al. 1999 and Beaumont et al. 2002)	Gelfand & Smith (1990), building on Geman & Geman (1984)
类型	simulation-based Bayesian inference	Bayesian computational sampler
开创性文献	Toni, T. & Stumpf, M. P. H. (2010). Simulation-based model selection for dynamical systems in systems and population biology. Bioinformatics, 26(1), 104–110.	Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A. & Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed.). CRC Press. ISBN: 978-1439840955
别名	hierarchical ABC, ABC for hierarchical models, multilevel ABC, population ABC	hierarchical MCMC, MCMC for multilevel models, Bayesian hierarchical MCMC, multilevel MCMC sampling
相关	4	6
摘要	Hierarchical ABC is a likelihood-free Bayesian inference method designed for multilevel data structures in which individual-level parameters are themselves drawn from a population-level distribution. By combining simulation-based rejection sampling with hierarchical pooling, it recovers both within-group and between-group posterior distributions without requiring a tractable likelihood function.	Hierarchical Markov chain Monte Carlo applies MCMC sampling to hierarchical Bayesian models, jointly drawing from the posterior over both observation-level parameters and the hyperparameters that govern them. This allows principled uncertainty propagation across all levels of a multilevel structure, from individuals to groups to population, using algorithms such as Gibbs sampling, Metropolis-Hastings, or Hamiltonian Monte Carlo.