手法を比較

	階層ベイズモデル平均法	階層ベイズ推論
分野	ベイズ	ベイズ
系統	Bayesian methods	Bayesian methods
提唱年	1999–2000s	1972 (Lindley & Smith); consolidated 1995–2013
提唱者	Hoeting, Madigan, Raftery, Volinsky (BMA foundation); multilevel extension developed across the late 1990s–2000s	Lindley & Smith; Gelman et al.
種類	Bayesian ensemble / model selection	Bayesian multilevel 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	multilevel Bayesian modeling, Bayesian hierarchical model, nested Bayesian model, partial pooling model
関連	6	6
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.	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.