方法对比

	Bayesian Regression	分层贝叶斯推断
领域	贝叶斯	贝叶斯
方法族	Bayesian methods	Bayesian methods
起源年份	—	1972 (Lindley & Smith); consolidated 1995–2013
提出者	—	Lindley & Smith; Gelman et al.
类型	Bayesian linear model	Bayesian multilevel model
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., 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	bayesian linear regression, probabilistic regression, bayesian regresyon	multilevel Bayesian modeling, Bayesian hierarchical model, nested Bayesian model, partial pooling model
相关	2	6
摘要	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.	Hierarchical Bayesian inference is a probabilistic modeling framework that organises parameters into levels, placing priors on the group-level parameters and hyperpriors on the parameters governing those priors. It enables partial pooling of information across groups, balancing the extremes of treating each group as independent or merging them into a single estimate.