方法对比

	贝叶斯模型平均 (Bayesian Model Averaging, BMA)	贝叶斯分层模型
领域	贝叶斯	贝叶斯
方法族	Bayesian methods	Bayesian methods
起源年份	1999	2006
提出者	Hoeting, Madigan, Raftery & Volinsky	Gelman & Hill (2006); Bayesian multilevel tradition
类型	Bayesian model averaging	hierarchical probabilistic 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), 382–401.	Gelman, A. & Hill, J. (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press.
别名	BMA, Bayesian model combination, Bayesian Model Ortalaması (BMA)	multilevel Bayes, Bayesian multilevel model, Bayesian HLM, partial pooling model
相关	5	4
摘要	Bayesian Model Averaging (BMA), formalised as a tutorial by Hoeting, Madigan, Raftery and Volinsky in 1999, addresses model uncertainty by averaging over all plausible model specifications rather than selecting a single best model. Each candidate model receives a posterior probability that reflects how well it fits the data given a prior, and predictions or coefficient estimates are formed as weighted averages across the entire model space. This approach reduces the bias and overconfidence that arise when a single selected model is treated as the true one.	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.