方法对比

	贝叶斯分层模型	Bayesian Regression
领域	贝叶斯	贝叶斯
方法族	Bayesian methods	Bayesian methods
起源年份	2006	—
提出者	Gelman & Hill (2006); Bayesian multilevel tradition	—
类型	hierarchical probabilistic model	Bayesian linear model
开创性文献	Gelman, A. & Hill, J. (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press.	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	multilevel Bayes, Bayesian multilevel model, Bayesian HLM, partial pooling model	bayesian linear regression, probabilistic regression, bayesian regresyon
相关	4	2
摘要	Bayesian hierarchical modelling, popularised by Gelman and Hill (2006), is a Bayesian approach to nested data structures — such as students within schools within districts — that estimates separate parameters at each level while allowing those levels to share statistical strength through a mechanism called partial pooling. Where a classical hierarchical linear model treats group means as fixed unknown quantities, the Bayesian version places hyperprior distributions on those group means so that information flows freely across levels, producing more reliable group-level estimates whenever any individual group has few observations.	Bayesian regression is a probabilistic version of linear regression that treats the model parameters as uncertain quantities. Instead of returning a single best-fit estimate, it combines prior knowledge with the observed data to produce a full posterior probability distribution for each parameter, from which credible intervals and predictions are read off.