手法を比較

	モデル比較のためのメトロポリス・ヘイスティングス法	ベイズモデル平均
分野	ベイズ	ベイズ
系統	Bayesian methods	Bayesian methods
提唱年	1970 (extended 1995)	1999
提唱者	W. K. Hastings (1970); extended for model comparison by P. J. Green (1995)	Hoeting, Madigan, Raftery & Volinsky
種類	MCMC-based model comparison	Bayesian model averaging
原典	Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57(1), 97-109.	Hoeting, J. A., Madigan, D., Raftery, A. E. & Volinsky, C. T. (1999). Bayesian Model Averaging: A Tutorial. Statistical Science, 14(4), 382–401.
別名	MH model comparison, Metropolis-Hastings Bayes factor estimation, reversible-jump Metropolis-Hastings, MH model selection	BMA, Bayesian model combination, Bayesian Model Ortalaması (BMA)
関連	4	5
概要	Metropolis-Hastings for model comparison uses the Metropolis-Hastings MCMC algorithm to explore both parameter and model space simultaneously, producing posterior probabilities for competing models and enabling Bayes factor estimation without requiring closed-form marginal likelihoods. The canonical extension — reversible-jump MCMC by Green (1995) — handles models of different dimensionalities within a single sampler.	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.