方法对比

	多层 Metropolis-Hastings	多层吉布斯采样
领域	贝叶斯	贝叶斯
方法族	Bayesian methods	Bayesian methods
起源年份	1953 (core); 1990s (multilevel application)	1990
提出者	Metropolis et al. (1953); hierarchical extension developed through 1980s–1990s Bayesian computation literature	Geman & Geman (1984); applied to multilevel models by Gelfand & Smith (1990)
类型	MCMC sampling algorithm	MCMC sampling algorithm
开创性文献	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	Gelman, A. & Hill, J. (2007). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press. ISBN: 978-0521686891
别名	hierarchical Metropolis-Hastings, multilevel MH, MH for hierarchical models, blocked Metropolis-Hastings	hierarchical Gibbs sampler, blocked Gibbs sampling for multilevel models, multilevel MCMC via Gibbs, Gibbs sampler for mixed-effects models
相关	6	6
摘要	Multilevel Metropolis-Hastings applies the Metropolis-Hastings MCMC algorithm to hierarchical (multilevel) Bayesian models, sampling jointly from group-level parameters and hyperparameters by proposing candidate values and accepting or rejecting them via a ratio that respects the full joint posterior across all levels of the model.	Multilevel Gibbs sampling applies the Gibbs MCMC algorithm to hierarchical (multilevel) Bayesian models, cycling through the conditional distributions of group-level parameters and population-level hyperparameters in turn. This exploits the conditional independence structure of the hierarchy to draw exact or near-exact samples from a posterior that would otherwise be analytically intractable.