方法对比

	层级贝叶斯模型平均	Bayesian Regression
领域	贝叶斯	贝叶斯
方法族	Bayesian methods	Bayesian methods
起源年份	1999–2000s	—
提出者	Extension formalised by Hoeting, Madigan, Raftery, and Volinsky; hierarchical application developed through 1990s–2000s Bayesian literature	—
类型	Bayesian model averaging within hierarchical models	Bayesian linear model
开创性文献	Hoeting, J. A., Madigan, D., Raftery, A. E., & Volinsky, C. T. (1999). Bayesian model averaging: A tutorial. Statistical Science, 14(4), 382–417.	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	HBMA, hierarchical BMA, multilevel Bayesian model averaging, Bayesian model averaging in hierarchical models	bayesian linear regression, probabilistic regression, bayesian regresyon
相关	5	2
摘要	Hierarchical Bayesian model averaging (HBMA) combines Bayesian model averaging with hierarchical model structure, averaging posterior quantities over a set of candidate models weighted by each model's posterior probability. Rather than selecting a single best model, HBMA propagates model uncertainty through a hierarchical framework, producing predictions and parameter estimates that honestly reflect uncertainty about which model is correct.	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.