手法を比較

	階層ベイズモデル平均法	Gibbs Sampling
分野	ベイズ	ベイズ
系統	Bayesian methods	Bayesian methods
提唱年	1999–2000s	1984
提唱者	Hoeting, Madigan, Raftery, Volinsky (BMA foundation); multilevel extension developed across the late 1990s–2000s	Stuart Geman & Donald Geman
種類	Bayesian ensemble / model selection	MCMC sampling algorithm
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.	Geman, S. & Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6(6), 721-741.
別名	ML-BMA, hierarchical Bayesian model averaging, multilevel BMA, Bayesian model averaging in multilevel models	Gibbs sampler, coordinate-wise MCMC, systematic scan Gibbs, blocked Gibbs sampling
関連	6	5
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.	Gibbs sampling is a Markov chain Monte Carlo algorithm that approximates a high-dimensional posterior distribution by repeatedly drawing each parameter from its full conditional distribution given all other parameters and the data. Because each draw is exact from a conditional — not a proposal that may be rejected — the sampler is efficient when those conditionals are available in closed form.