手法を比較

	階層ベイズモデル平均法	ベイズ回帰
分野	ベイズ	ベイズ
系統	Bayesian methods	Bayesian methods
提唱年	1999–2000s	—
提唱者	Hoeting, Madigan, Raftery, Volinsky (BMA foundation); multilevel extension developed across the late 1990s–2000s	—
種類	Bayesian ensemble / model selection	Bayesian linear model
原典	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., 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
別名	ML-BMA, hierarchical Bayesian model averaging, multilevel BMA, Bayesian model averaging in multilevel models	bayesian linear regression, probabilistic regression, bayesian regresyon
関連	6	2
概要	Multilevel Bayesian model averaging (ML-BMA) extends classical Bayesian model averaging to grouped or hierarchically structured data. Rather than committing to a single multilevel model specification, it computes a weighted average of predictions and parameter estimates across a set of candidate multilevel models, weighting each model by its posterior probability given the data. The result accounts simultaneously for uncertainty in the grouping structure, fixed effects, random effects, and covariate selection.	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.